Circuit Design for Linearizing Transmitter Sim Chan Kuen NATIONAL UNIVERSITY OF SINGAPORE 2003 Circuit Design for Linearizing Transmitter Sim Chan Kuen, (B. Eng., Nanyang Technological University) DEPARTMENT OF ELECTRICAL ENGINEERING A THESIS SUBMITTED FOR THE DEGREE OF MASTER OF ENGINEERING NATIONAL UNIVERSITY OF SINGAPORE 2003 i Acknowledgement I would like to take this opportunity to express my warmest thanks to many people who have contributed towards the production of this thesis. In particular, I thank my supervisors, Dr. Michael Chia Y. W. and Prof. Lye Kin Mun. I thank Dr. Michael Chia for his guidance and support. He spent a tremendous amount of time teaching me discussing the research problem and checking this thesis. I thank my friends and colleagues in the Transceiver System group of Institute of Infocomm Research (I2R). They advised me throughout the course of work and in completion of this thesis. Lastly, I thank my family for their constant support and care. ii Contents Acknowledgement i Contents ii List of Figures v List of Tables viii Summary ix Chapter 1 Introduction 1 1.1 Background 1 1.2 Power Amplifier 3 1.3 Objective 5 1.4 Thesis Organization 5 Power Amplifier Characteristics and Linearization 7 2.1 Classification of Power amplifier 7 2.2 Distortions of Power Amplifier 9 2.3 Modeling of Power Amplifier 13 2.4 Power Amplifier Testing 14 2.4.1 Two Tones Test 14 2.4.2 Noise-Power-Ratio (NPR) 15 2.4.3 Adjacent Channel Power Rejection (ACPR) 15 2.4.4 Emission Mask 16 Chapter 2 2.5 Linearization 17 2.5.1 Cartesian Feedback 17 2.5.2 Feedforward 19 iii Chapter 3 2.5.3 Envelope Elimination and Restoration 21 2.5.4 Linear Amplification with Non-Linear Components 22 2.5.5 Predistortion 24 The Design of Analog Predistorter 27 3.1 Introduction 28 3.2 System block of the analog predistorter 32 3.3 System Consideration 35 3.4 Circuit Implementation 39 3.4.1 Analog Multiplier 39 3.4.1.1 Brief Survey 39 3.4.1.2 Implementation of Analog Multiplier 43 3.4.2 Transconductance cell 50 3.4.3 Transimpedance cell and Output Buffer 52 3.5 Simulation 54 3.6 Layout 56 3.7 Completed Chip 59 Tests Results for the Analog Predistorter 60 4.1 Predistorter Performance 61 4.2 Low-IF Analog predistortion 62 4.2.1 Two-Tone Tests 62 4.2.2 Multi-carrier signals 68 4.2.3 OFDM signals 70 4.2.4 IS95 73 Chapter 4 4.3 Baseband analog predistortion 75 iv 4.4 Chapter 5 Analog predistortion for Radio Over Fiber System (ROF) 80 Conclusions 87 Bibliography 90 Appendix 95 v List of Figures 1.1 Modern Transmitter Architecture 2 2.1 Basic Circuit Diagram for Power Amplifier 8 2.2 Power Amplifier characteristics 11 2.3 Intermodulation Distortion of Power Amplifier 11 2.4 Noise Power Ratio Testing 15 2.5 ACPR 15 2.6 Emission Mask 16 2.7 Cartesian Feedback 18 2.8 Feedforward Linearization 19 2.9 Envelope Elimination and Restoration 21 2.10 Linear Amplification with Non-Linear Components 22 2.11 Basic principle of Predistortion 24 3.1 Implementation of Predistorter at different stage of the Transmitter 31 3.2 Block of the 3rd Order Analog Predistorter 35 3.3 A Basic Bipolar implementation of Analog Mulitplier 40 3.4 Two general method of implementing analog multiplier in CMOS 41 3.5 Analog Multiplier 44 3.6 The complete analog multiplier 47 3.7 Simulated Result of the multiplier 48 3.8 Simulated distortions in multiplier 49 3.9 Transconductance cell 51 3.10 Simulated results of the transconductance cell 52 3.11 Transimpedance cell 53 vi 3.12 Output Buffer 54 3.13 Die photo of the predistorter 59 4.1 Pout vs Pin of the power amplifier 62 4.2 A Two Tone Test performed on the power amplifier 63 4.3 Test setup for low-IF predistorter 64 4.4 Before Linearization (Two-tones test at low-IF) 65 4.5 After Linearization (Two-tones test at low-IF) 65 4.6 A two-tones test with varying input power 66 4.7 Multi-Carrier Test(Before Linearization) 68 4.8 Multi-Carrier Test(After Linearization) 69 4.9 Frequency spectrum at the input of the power amplifier (Before Linearization) 4.10 Frequency spectrum at the ouptut of the power amplifier (Before Linearization) 4.11 71 Frequency spectrum at the input of the power amplifier (After Linearization) 4.12 71 72 Frequency spectrum at the output of the power amplifier (After Linearization) 72 4.13 IS95 signals (Before Linearization) 74 4.14 IS95 signals (After Linearization) 74 4.15 Test setup of baseband predistortion 76 4.16 Overall output spectrum for baseband predistortion two-tones test (before linearization) 4.17 77 Zooming on the frequency spectrum around the two tones for baseband predistortion two-tones test (before linearization) 77 vii 4.18 Overall output spectrum for baseband predistortion two-tones test (after linearization) 4.19 78 Zooming on the frequency spectrum around the two tones for baseband predistortion two-tones test (after linearization) 78 4.20 Test Setup using predistorter in Radio Over Fiber system 80 4.21 Overall output spectrum for ROF predistortion two-tones test (before linearization) 4.22 Zooming on the frequency spectrum around the two tones for ROF predistortion two-tones test (before linearization) 4.23 81 Overall output spectrum for ROF predistortion two-tones test (after linearization) 4.24 81 82 Zooming on the frequency spectrum around the two tones for ROF predistortion two-tones test (after linearization) 82 4.25 Two-tones test for ROF system 83 4.26 Multi-Carrier Test for ROF system(Before Linearization) 85 4.27 Multi-Carrier Test for ROF system(After Linearization) 85 viii List of Tables 4.1 Performance of Predistorter 61 4.1 Comparison of two-tone test results performed by different design 67 Chapter 1 Introduction 1.1 Background The primary purpose of any wireless communication systems is to transmit or receive information. The information could be in any form such as speech, pictures or data. In the area of cellular and personal communication service (PCS) systems, there is a trend of transmitting data and video instead of merely speech. In third generation (3G) cellular systems, such as WCDMA system, the data rates that could be transmitted will enable even video to be transmitted through cellular systems. With higher data rates of the 3G systems, it will open up a whole range of services to the consumers. One of the major enabling device for 3G or future cellular systems is the transceiver. Page 2 It consists of the two major blocks, the receiver and transmitter. The receiver receives information from air. Whereas the transmitter transmits information generated by the cellular terminals to the air. It is thus front end of cellular communication systems. I DAC Local Oscillator VGA Antenna 900 Phase Shifter Q RF Power Amplifier DAC Figure 1.1 Modern Transmitter Architecture The block diagram of the modern transmitter is shown in Fig 1.1 [1]. The I and Q channels generated by the baseband is converted into analog signals by the Digital-toAnalog converters (DAC). It will then be low pass filtered and upconverted by the mixers to radio frequencies. The signals are amplified by the variable gain amplifiers (VGA). The final amplification of the signals is by the power amplifier. It will drive the antenna and transmitted to the air. Page 3 1.2 Power Amplifier One of the major blocks of the transmitter is the power amplifier [2]. This component consumes the most power of the transceiver [3]. For example, RF MicroDevices’s RF2161 [4] or Raytheon’s RTPA5250-130 [5] consume 0.4W and 0.66W respectively. To achieve higher data rate and be spectrally efficient, communication systems use linear modulation for example QAM (Quadrature Amplitude Modulation). Linear modulation allows more data to be send within a given bandwidth. However, linear modulation will have varying envelope at the output of the power amplifier. To properly amplify the signal, the power amplifier must be linear. But linear power amplifier consumes a lot of power compared to non-linear power amplifier. A non-linear power amplifier will cause undesirable distortions to the transmitted signal. This will lead to an increase in the overall error rate of the communications system. Not only that, a non-linear power amplifier will exhibit spectral regrowth [1]. This will cause distortions to adjacent channels. It is possible to design a class A power amplifier to meet the linearity requirements for modern communication systems. But class A power amplifier is highly inefficient in power. Theoretically the efficiency of the class A amplifier is 50% [1]. But in actual implementation, the efficiency of the power amplifier is much lower than 50%. Page 4 Power efficiency of the power amplifier will affect the power consumption of the transmitter. Being the most power consuming block of the transceiver, any reduction in power consumption will reduce the power consumption of the whole transceiver system. A reduction of power consumption will increase the talk time of the communication equipment. This is especially important for cellular mobile phones. Therefore there is a compromise between the efficiency and linearity of the power amplifier. Generally, class AB power amplifier is good compromise between linearity and efficiency. Page 5 1.3 Objective The objective of this research is to improve the linearity of the Radio Frequency (RF) power amplifier so as to operate the power amplifier near the peak efficiency so as to increase the talk time of the mobile handsets. 1.3 Thesis Organization The thesis is organized as follows: In chapter 2, the general characteristic of the power amplifier is explained. It shows how the power amplifier could be modeled, the distortions it creates and the different metrices to measure the linearity of the power amplifier. In this chapter, the reader will also acquaints himself the general techniques that are used to improve the linearity of the power amplifier namely feedback, feedforward and predistortion. The next chapter, chapter 3, the design of the new analog predistorter is described. This shall include the architecture and circuit. In chapter 4, the chip was used to linearise an actual RF power amplifier. The chip was tested at IF and baseband. Two-tone test was used to test the improvement in the linearity of the power amplifier. Then different linear modulations were injected into predistorter. Page 6 The use of the predistorter was then extended to a Radio Over Fiber (ROF) system. The result for the new usage of the predistorter was also illustrated. Finally, chapter 5 presents a summary of the work done in linearization of the power amplifier. Chapter 2 Power Amplifier Characteristics and Linearization In this chapter, the different classes of power amplifier, the characteristics and the distortions caused by the power amplifier would be briefly discussed. The modeling of the power amplifier will also be covered. Some of the existing methods of linearizing the power amplifier will be presented. 2.1 Classification of Power amplifier There are different classes or types of power amplifiers namely Class A, B, C, E and F. The above different classes could be grouped into two [3]. The first group, class A, B and C, are power amplifiers that use the transistors as current sources. The second group, class E and F, use transistors as switches. Page 8 DC RFC Filtering/ Matching Network Vin Figure 2.1 RL Basic Circuit Diagram for Power Amplifier Figure 2.1 shows the basic circuit diagram for all the power amplifiers [1]. The radio frequency choke (RFC) feeds the DC power to the drain of the BJT. It is to provide low impedance for the bias but high impedance for a.c. signals. The BJT could also be replaced by other types of transistor e.g. NMOS. Filters and matching network are connected at the output of the power amplifier. The filtering network is to reject all undesired out of band signals. The matching network is required to deliver sufficient power to the load, RL. In the first group, class A, B and C, the transistors act as current sources. The transistor will either sink or source current to the load. The differences between class A, B and C is in their conduction angles. In class A, the power amplifier is biased such that the current will conduct at all times. But the conduction angle is 180 degrees and below 180 degrees Page 9 for class B and C power amplifiers respectively. The linearity for class A power amplifiers is the best followed by B and C. But the power efficiency is the lowest for class A and highest for class C. A compromise between linearity and power efficiency is met by class AB power amplifiers. Class E [6] and F power amplifiers are non-linear power amplifiers. The transistors in Class E power amplifiers act as a switch rather than a current source. In an ideal switch, when it is ON, the voltage across the switch is zero and the current will be the maximum. When the switch is OFF, the voltage should rise to the maximum while the current is zero. Therefore the ideal switching power amplifier has 100% efficiency. In Class F amplifier, the filtering/matching network has resonances at one or more harmonic frequencies including the fundamental carrier frequency. The filtering/matching network will shape the output collector voltage of the power amplifier to a square wave like waveform [7]. Generally, Class E and F power amplifiers are more efficient compared to Class A to C power amplifiers. However, they generate more distortions than Class A to C power amplifiers. 2.2 Distortions of Power Amplifier Amplitude Distortion Ideally the output of the power amplifier should follow the equation as shown in (2.1). The output power, Pout, is K times of the input power, Pin. K is a fix constant. Pout = K * Pin --------- (2.1) Page 10 Figure 2.2 compares the ideal response at the output of the power amplifier and the practical amplifier. In pratice, there is a limited range where the power amplifier is able to amplify the signal presented in the input. The value of the K, as in (2.1), changes as the input of the power amplifier increases. When input power exceeds a certain level, the power amplifier will be saturated. The non-linearity of the input and output of the power amplifier is also termed as AM-AM conversion. However, the efficiency near the saturation point is the highest. One of the ways to compare the linearity of different amplifiers is find the P1dB point. This is the point where the output power of the actual power amplifier is 1dB below the Output Power ideal response of a power amplifier. Ideal P1db Practical Input Power Figure 2.2 Power Amplifier characteristics Page 11 The most serious consequence of the amplitude non-linearity is intermodulation distortion. Figure 2.3 illustrates this distortion. Amplitude Amplitude Power Amplifier Frequency Frequency Figure 2.3 Intermodulation Distortion of Power Amplifier Ideally when two frequency tones are injected into the power amplifier, the output of the power amplifier will have exactly the same two frequency tones but with amplified amplitude. Intermodulation distortion causes the power amplifier to produce extra frequency components other than the two original frequency components. These additional frequency components will increase in amplitude as the power amplifier is approaching its saturation point and they cannot be filtered out because it is within the bandwidth of the system. Due to intermodulation distortion, there is spectral regrowth at the output of the power amplifier. This will cause interference of adjacent channels. Page 12 Phase Distortion The other subtle aspect of linear power amplifier is that it should have a linear phase response [7]. It meant that the time delay between the input and output of the power amplifier should be the same across its bandwidth. If the time delay is different the output of power amplifier will be distorted. One of the phase distortion caused by the power amplifier is known as AM-PM conversion [7][8]. It happens when the input modulated signal caused a phase change in the output of the power amplifier. The modulated signal will cause extra frequency components at the output of the power amplifier. The distortions discussed above do not take into account of the memory effects of the power amplifier [9][10]. For a memoryless power amplifier, it has the same level of distortions throughout its bandwidth. But the actual power amplifier will have different AM-AM and AM-PM distortions at different parts of its bandwidth. Generally, using the assumption of memoryless power amplifier, it is possible to model the typical distortions in the power amplifier. Page 13 2.3 Modeling of Power Amplifier The simplest way to model the power amplifier is by using a power series [11] as shown in (2.2). Vo = a1Vi (t ) + a3Vi 3 (t ) + a5Vi 5 (t ) + ........ . --------(2.2) Vo (t ) and Vi (t ) are the output and input of the power amplifier respectively. an are the complex coefficients of the power amplifier. These coefficients give you the gain of the various frequency components. It is assumed that the power amplifier has a narrow bandwidth compared to the RF frequency that it is being transmitted. Therefore even order frequency components do not fall into the bandwidth of the transmitter and could be filtered out. Using the power series, it is able to model the 1db compression point, gain and phase distortion. But the distortion caused by the higher order in the power series is very low. The most serious distortion is caused by third and maybe the fifth order in the power series. Therefore most power amplifier could be modeled adequately by a fifth order power series. There are other models available such as [12]. The common methods in power amplifier modeling are given in [7]. But these models tend to be more complex than the power series and no comparisons of accuracy of different models are given. Page 14 2.4 Power Amplifier Testing In order ascertain the linearity of the power amplifier, it should be measured using two tones test, noise power ratio, adjacent channel power rejection and emission mask. These tests give an indication of the non-linearity in power amplifier and could be adapted to test the linearity of wideband signal (i.e. WCDMA) and multi-carrier system (i.e. OFDM). 2.4.1 Two Tones Test The two-tone test is the standard test for linearity of the power amplifier. Figure 2.6 shows how the two-tone test is performed. It is to input two frequency tones to the power amplifier. For a narrow band system, the frequency spacing of the two tones is estimated to be the bandwidth of the transmitter. At the output of the power amplifier, other frequency components, caused by the intermodulation distortion, will be measured by a spectrum analyzer. As the input power to the power amplifier is increased, the extra frequency components will also increase, normally at a faster rate than fundamental two tones. Third order intermodulation distortion (IMD3) is the most serious distortion. The two-tones test is the simplest test to be performed on the power amplifier. Also it qualitative of the improvement in linearity before and after linearization is implemented. Page 15 2.4.2 Noise-Power-Ratio (NPR) Amplitude Amplitude Power Amplifier Frequency Frequency Figure 2.4 Noise Power Ratio Test Noise Power Ratio Test [7] is normally used to test the linearity of multi-carriers communication systems. The center channel is switched off. Non-linearity in the power amplifier will produce distortions hence will fill up the center channel. By observing the level of increase at the center channel, it is possible to measure the distortions introduce by the power amplifier. 2.4.3 Adjacent Channel Power Rejection (ACPR) Amplitude B1 B2 Frequency Figure 2.5 ACPR Page 16 Adjacent channel power ratio (ACPR) [7][13] is a measure of the degree of spreading to adjacent channel. Referring to Figure 2.5, ACPR is defined as the power within a specified bandwidth, shown as B1 in Figure 2.5, divided by the power at the adjacent channel, indicated as B2 in Figure 2.5. It gives us a measure of the spectral regrowth of the power amplifier by comparing the ACPR at the input and output of the power amplifier. Power 2.4.4 Emission Mask Emission Mask Output Signal Frequency Figure 2.6 Emission Mask In most cellular standards, it defines a relative value to the channel output signal the spurious emissions must be below. It could be view as an emission mask at the spectrum analyser shown in Figure 2.6. The output signal from the power amplifier must be below the emission mask. It is a simple test for compliance of the power amplifier emissions to the cellular standard. But every cellular standard has a different emission mask. Page 17 2.5 Linearization Linearization can be used to improve the linearity and efficiency of the power amplifier. In this section, the five methods are discussed on the linearization of the power amplifier. They are a. Cartesian Feedback b. Feedforward c. Envelope Elimination and Restoration d. Linear Amplification with Non-Linear Components e. Predistortion Each method has its limitations. It is implemented in different situation depending on a various factors such as modulation bandwidth, complexity of the method, cost etc. 2.5.1 Cartesian Feedback Feedback has been traditionally used to linearize an audio frequency amplifier. It was invented and patented by H. S. Black [14] in 1928. It has since used widely in low frequency analog circuit to linearize a non-linear amplifier. The operational amplifier (op amp) is an excellent example of feedback. The op amp itself has a very high gain but is non-linear. But using feedback, it is able to create a linear amplifier but at a lower gain. However, applying feedback directly to the RF power amplifier will not reduce the Page 18 distortions significantly because normally RF power amplifier does not have enough gain at high frequency. Also there is a problem of stability at RF frequency. A modified version of the feedback is the Cartesian Feedback [7][15]. Figure 2.7 shows the general block diagram. I + Power Amplifier - 0 90 Q Coupler + Phase Shifter 0 Attenuator 90 Figure 2.7 Cartesian Feedback Part of the output of the power amplifier is sampled and demodulated back into I and Q channel. It is feedback to the input to create an error signal. This error signal is filtered out and modulated to the RF frequency and input to the power amplifier. The gain of the power amplifier will definitely decrease due to the feedback. But it might decrease the distortions of the power amplifier drastically. Page 19 The main problem with Cartesian Feedback is the control of the phase shifter. The feedback signal should not be in phase with the input otherwise it would lead to instability. In order that the feedback signal to be out of phase with the input, the phase shifter must be adjusted to meet this criteria. If the modulation bandwidth of the input signal is wide, the phase changes from one part of the bandwidth to another. Therefore the phase shifter must be able to automatically change its phase. The control of the phase shifter is troublesome and not easily implemented. The other problem is that the feedback path must be linear. The power amplifier would amplify any distortions in the feedback path. Hence the Cartesian Feedback is currently used in narrowband systems. 2.5.2 Feedforward Time Delay RFOUT Coupler RFIN Main Power Amplifier Power Splitter Error Amplifier Time Delay Figure 2.8 Feedforward Linearization Figure 2.8 shows the general block diagram of the feedfoward linearization [16]. The RF input is split into two branches. The main power amplifier will amplify the input signal Page 20 with all the distortions of the power amplifier present. The other branch goes through a time delay. A directional coupler will then couple part of the power into the second branch. This will cancel out the linear portion of the signal, leaving the distortions to be amplified by the error amplifier. At the output of the feedfoward system, the distortions amplified by the error amplifier will cancel the distortions produce by the power amplifier. Therefore at its output, it will have a linearized RF signal. One of the problems in the feedfoward linearization is the time delay. The power amplifier has to be characterize thoroughly so as to be able determine the time delays of various components. It is unable to adapt to the changing environment if it not modified. Some research work had been done in this area [17]. The other problem is that it requires an error amplifier. This adds to the power consumption of the overall system. Also the couplers and splitters used are passive, therefore lossy, components. This will also decrease the efficiency of the overall system. Feedforward linearization is an open loop linearization. Therefore it has much greater bandwidth compared to feedback linearization. It is possible to obtain good linearity performance. It is normally used in base stations. Page 21 2.5.3 Envelope Elimination and Restoration Figure 2.9 Envelope Elimination and Restoration Modulated signal at the output of the power amplifier could be written as v(t ) = a(t ) cos(ωt + φ (t )) ------(2.3) where v(t ) is the output signal, a(t ) is the envelope of the modulated signal and φ (t ) is the phase of the modulated signal. The idea of Envelope Elimination and Restoration (EER)[1] of linearization is to decompose the modulated signal into an envelope signal and phase-modulated signal. This could be amplified individually and combined at the end. This is shown in the illustration in Figure 2.9. The input signal is split into its envelope signal and phase-modulated signal using an envelope detector and limiter respectively. The phase-modulated signal is injected into the input of the switching power amplifier such as Class E amplifier. The envelope signal is amplified and is used to drive Page 22 the supply line of the switching power amplifier. Therefore at the output of the switching power amplifier, the modulated input signal is not only amplified but also its envelope and phase is restored back. The advantage of this method is that we could use a nonlinear switching power amplifier thereby greatly improving the efficiency of the power amplifier. However, there are a few problems using this method. Firstly, to properly restore the modulated signal at the output of the power amplifier, the phase shifts for the envelope signal and the phase-modulated signal must be the same. This is difficult to accomplish as the circuits used in the envelope signal and phase-modulated paths are very different. Secondly, using a limiter to extract the phase-modulated signal introduce additional AMto-PM distortions. 2.5.4 Linear Amplification with Non-Linear Components Figure 2.10 Linear Amplification with Non-Linear Components Page 23 The idea for Linear Amplification with Non-Linear Components (LINC)[1][7] linearization is to decompose the modulated signal given in Equation (2.3) into two phase-modulated signals given in (2.4) v1 = 0.5Vo sin (ω t + φ (t ) + θ (t )) v1 = −0.5Vo sin (ω t + φ (t ) − θ (t )) -----(2.4) where θ (t ) = sin −1 [a(t ) / Vo ] and Vo is a constant. The block diagram for LINC is shown in Figure 2.10. The input signal is split into two phase-modulated signals by the signal separator. Then they will be amplified individually non-linear power amplifier such Class E amplifier. Finally, the amplified signal is restore by combining the output signal of the non-linear power amplifier together. The disadvantage of this method is that firstly it is difficult to implement the signal separator in analog or RF domain. The circuits that had to be implemented are non-linear. Secondly the phase delay of the two phase modulated signals must be the same. Thirdly, the adder at the end must have high isolation between the two non-linear power amplifiers else it will distort the final output signal. Page 24 2.5.4 Predistortion Power Amplifier Predistorter Output Input Figure 2.11 Basic principle of Predistortion Figure 2.11 shows the basic principle of predistortion. A non-linear device, in this case a power amplifier, could generate a linear output, if there is a predistorter that is inserted before it. The characteristics of the predistorter must be the inverse of that from the power amplifier. This technique is very general and is applicable in lot of applications. The modeling of the non-linear device is crucial so that it is possible to generate a predistorter that eliminate or reduce the distortions. As discussed in section 2.3, the power amplifier could be modeled as an odd order power series. If it is restricted to a third order power series, it could be written as in (2.5). Vo = a1Vi + a3Vi3 ------(2.5) Page 25 where Vo and Vi are the output and input of the power amplifier respectively. an are the coefficients of the power amplifier. If the predistorter has a similar third order series as shown in (2.6). VP = β1V’i + β3V’i3 --------(2.6) where VP and V’i are the output and input of the predistorter respectively. βn is the coefficients of the predistorter. Since the predistorter is inserted before the power amplifier, then Vi =VP. Therefore the output of the power amplifier is Vo = a1β1 V’i + [a1β3 + a3β13] V’i3 + 3 a1β12β3 V’i5 + 3 a3β1β32V’i7 + a3β33 V’i9 (2.7) From (2.7), it is possible to draw some possible implications using predistortion. Firstly, it is possible to reduce the third order distortions by proper selection of the coefficients of the predistorter. Theoretically, by choosing the correct coefficients, the third order distortion could be eliminated. Secondly, as a third order predistorter, fifth, seventh and ninth order distortion starts to appear. This is not present when the power amplifier is used alone. It is possible to eliminate these higher order terms using a higher order predistorter. But even higher order distortions terms will start to appear. In practice, these higher order terms are generally much lower in amplitude compared to the third order distortion. The combination of the predistorter and power amplifier will still improve the linearity of the overall power amplifier. In an actual power amplifier, it does not behave Page 26 exactly in manner described by a power series. Therefore the third order predistorter will not eliminate all the third order distortion. One of things to take note is that it is quite impossible to linearize the power amplifier if it is operating at the saturation point. The power series model is impossible to describe power amplifier near or at the saturation point. The third order distortions generated by the power amplifier is the most serious. In order to maximize the power efficiency of power amplifiers, it will be operating near to its saturation point. Performing a two-tone test at the saturation point, the third order distortions would have the highest distortion power levels compared to the rest of the distortions. If the RF power amplifier is used in a multi-carrier system, the distortions generated is even predominantly third order [18]. The fifth and higher order distortions would also be present but these distortions have lower power levels. The predistortion linearization is an open loop linearization method. Therefore it has a wide bandwidth. Good linearity is able to obtain from this method. The most troublesome problem is to find the correct coefficients for the power amplifier. Also the power amplifier characteristics will drift in time, the predistorter should be able to track these changes and modify the coefficients to maximize the linearity of the power amplifier. Chapter 3 The Design of Analog Predistorter Predistortion is simple and effective method of linearizing the power amplifier. Also the power amplifier could be modelled as an odd order power series. Simply using this odd order power series model, the predistorter is able reduce the distortion by introducing a similar odd power series before the power amplifier. In this chapter, the power amplifier’s model is slightly modified. Using the modified model, an analog predistorter was designed and fabricated to linearize the power amplifier. The major blocks of the design and different considerations of the blocks are discussed. Finally the simulation, layout and die photo of the chip is presented. Page 28 3.1 Introduction The power amplifier model introduced in the previous chapter does not take into the account the phase distortion. A more accurate model for the power amplifier is to use complex coefficients so that they are complex values [19] as shown in (3.1). Po = a1Pi + a3Pi3 + a5Pi5 + …….. 3 5 = (a11 + j a11)P i + (a31 + j a31) Pi + (a51 + j a51) Pi + …… (3.1) In this modified model, the power series is still an odd order function. All the even order distortions would be filtered out at the output of the power amplifier thus the distortion it causes is not as significant as odd order distortions. The odd order power series is able to model the intermodulation distortion (IMD). However, the model is still a memoryless model. Since the power amplifier could be more accurately modeled using complex coefficients, the predistorter should also use complex coefficients to improve the linearity of the power amplifier. The third order intermodulation distortion (IMD3) is the most serious distortion generated by the power amplifier. If the predistorter is able to reduce the IMD3 of the power amplifier, the linearity of the power amplifier would be greatly improved. This is especially true in multi-carrier systems[18] where the distortions is caused predominantly by IMD3. For example, in [20] 3 carriers were injected to a power amplifier. The measured IMD3 was at least 31dB greater than the IMD5. In practical Page 29 power amplifier, the coefficients a 5 33dbc compared to the fundamental two-tone signal Page 62 4.2 Low-IF Analog predistortion 4.2.1 Two-Tone Tests The RF power amplifier used is RF2161 manufactured by RF Micro Devices [4]. It was firstly characterised before the predistorter was added. A power detector was used to measure the Pout verses Pin plot of the power amplifier and is shown in Figure 4.1. The power amplifier has a linear gain of about 27dB till it saturates at about 27dBm. A higher input power will not drive the power amplifier to deliver power greater than its saturation point. 29 27 Pout(dbm) 25 23 21 19 17 15 -15 -10 -5 0 5 10 Pin(dbm) Figure 4.1 Pout vs Pin of the power amplifier A 2-tone test was performed on the power amplifier alone. The power levels of the fundamental, third order intermodulation distortion (IMD3) and the fifth order intermodulation (IMD5) were shown in Figure 4.2. The output of the power amplifier Page 63 was attenuated by 20dB before it was measured by the spectrum analyser. It shows a typical graph of a power amplifier. The gradient of the IMD5 is the highest followed by IMD3 and then the fundamental power. The greatest distortion is caused by IMD3 because the power level is the highest. 10 0 -10 Pout(dbm) -20 Pout(dbm) Fundatmental Pout(dbm) IMD3 Pout(dbm) IMD5 -30 -40 -50 -60 -70 -80 -25 -23 -21 -19 -17 -15 -13 -11 -9 -7 -5 -3 Pin(dbm ) Figure 4.2 A Two Tone Test performed on the power amplifier The predistortion chip was tested at low-IF frequency. The input signal is upconverted to IF frequency at 20Mhz. The predistorter accepts the in phase and quadrature phase of the input signal. It then predistorts the signal and is upconverted again to RF frequency. Finally it is injected to the RF power amplifier. The test setup is shown in Figure 4.3. Page 64 Source (HP ESGD) 20Mhz RF Amplifier RF2161 Predistorter Spectrum Analyser 90 degree phase shifter LO Figure 4.3 Test setup for low-IF predistorter A two-tone test was performed before and after the predistorter chip was added. The coefficients that were used to reduce the distortions caused by the power amplifier were manually tuned to obtain the best results for all the tests. In the two-tone test, the IMD3 of the power amplifier for every power level were firstly noted down using the spectrum analyser without the predistorter added. Then the predistorter was added and the coefficients were tuned to get the lowest level of IMD3. These coefficients were tuned by setting the voltage levels at the input of the analog multipliers in the predistorter chip. The coefficients could be tuned from -400mV to 400mV. This is set by external variable potentiameter at the testing PCB board where the predistorter chip was mounted. The potentiameter has a tolerance of 10 percent. This tolerance of the potentiometer will limit the sensitivity of the coefficients when there is a change in the IMD3 of the power amplifier. For every model of power amplifier, the distortion it generates is different and therefore the predistorter has to calibrate to that power amplifier. In these series of tests, we calibrate to the power amplifier RF2161 from RF Micro Devices. Page 65 The results for the two-tone test are shown in Figure 4.4 and 4.5. Figure 4.4 Before Linearization (Two-tone test at low-IF) Figure 4.5 After Linearization (Two-tone test at low-IF) From the results, the IMD3 had decreased by 16dB after the predistorter was inserted into the transmitter chain. This is a significant drop in distortions by a third order analog predistorter. The IMD3 contribute the most serious distortion at the output of the power amplifier. The predistorter therefore has significantly improved the linearity of the power amplifier. To show the improvement the predistorter has on the linearity of the power amplifier, the input power levels of two tones were swept over a certain range. The 3rd order intermodulation was measured before and after linearization. The coefficients that were used to reduce the distortions were manually tuned. For each output power level, Page 66 the coefficients had to be adjusted for optimum performance. The result is shown in Figure 4.6. There was a 20dB attenuator before the spectrum analyser and therefore the results were scaled down. 0 -10 Output Power (dbm) -20 -30 -40 Before Linearization(Fundamental) After Linearization(Fundamental) Before Linearization(IMD3) After Linearization(IMD3) -50 -60 -70 -80 -15 -14 -13 -12 -11 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 Input Power (dbm) Figure 4.6 A two-tone test with varying input power From Figure 4.6, it was clearly seen that the predistorter is able to reduce the 3rd order intermodulation significantly. The predistorter was able to reduce IMD3 to -70dBm for a range of input power. However, there is a limit to the reduction of the distortion by the predistorter. From the diagram, when the input power was about –6 dBm, the predistorter could no longer effectively linearize the power amplifier. The distortion levels rises dramatically when the input power is greater than –6dBm. This is because the predistorter chip has a finite input power dynamic range. If the input power injected into the predistorter is out its usable range, it would generate more distortions at the output of the power amplifier instead linearizing it. Page 67 Similar work done in analog predistorter [19][22][30], has used the two-tone test as the basic test for the linearity of the power amplifier. They have shown to be able to reduce the IMD3 from the power amplifier by 30dB using a fifth order complex analog predistorter. From Figure 4.5, the third order complex analog predistorter that was designed could reduce the IMD3 by more than 20dB. This suppression could be enough for some types of power amplifier to meet its specifications. Also IMD3 is the most serious distortion for most power amplifiers. The number of circuits required for a third order complex analog predistortion is definitely lesser, generating lower noise and using lesser current. The predistorter implemented by [19][22][30] did not give results using an actual RF power amplifier. [19] and [30] has shown its results at an IF of 200Mhz and [22] was tested at 21.4Mhz. The distortion for an actual RF power amplifier would be more serious than low frequency amplifiers. A summary of the two-tone test by [19][22][30] is given in Table 4.2. However in this design, it is not possible to reduce the IMD5 of the power amplifier. Remarks The amplifier was a Class A amplifier operating at 200Mhz [22] The result was for an amplifier operating in Class AB mode at 21.4Mhz. [30] IMD3 Reduction:>30dB The amplifier was a Class A IMD5 Reduction:5dB amplifier operating at 200Mhz Current Work IMD3 Reduction: 27dB An actual RF power amplifier was used. The amplifer is a Class AB power amplifer operating at 1.83Ghz. Table 4.2 Comparison of two-tone test results performed by different design [19] IMD Reduction IMD3 Reduction: >30dB IMD5 Reduction: 10dB IMD3 Reduction:30dB IMD5 Reduction:10dB Page 68 4.2.2 Multi-carrier signals Next, multi-carrier signal was used as the test signal. Noise Power Ratio (NPR) was used as a measure third order intermodulation distortion (IMD3). Five sub-carriers were used in this test. However, the center sub-carrier was switched off. Each of the sub-carriers were modulated BPSK with a random data rate. The sub-carrier spacing is 100khz with a total bandwidth of 500khz. The center frequency is 1.87Ghz. The test results are shown in Figure 4.7 and 4.8. The results were normalized. Figure 4.7 Multi-Carrier Test(Before Linearization) Page 69 Figure 4.8 Multi-Carrier Test(After Linearization) Before linearization, the power level of the center tone was –30.47dBm. It is shown in Figure 4.7. Since the center sub-carrier was switched off, the power level of perfectly linear power amplifier will be very low. But the distortions caused by the power amplifier falls into the center switched off sub-carrier. The power level will give an indication of the distortions by the power amplifier. After linearization, the power level at the center sub-carrier decreased to –39.32dBm. There was a reduction in power level of the center sub-carrier of –8.85dB after linearization. From this test, it is shown that the complex analog predistorter is functioning. The predistorter works with an actual modulated data instead of pure tones shown in twotone test. Also shown in Figure 4.7 and 4.8, most of the out of band distortions also decreased due to the predistorter. Page 70 4.2.3 OFDM signals The next test, the input was an Orthogonal Frequency Division Multiplexing (OFDM) signal similar to 802.11a. It has a total of 52 sub-carriers occupying a 2Mhz information bandwidth. The test setup used was shown in Figure 4.3. The input signal, which has an information bandwidth of 2Mhz, was upconverted to a low IF of 20Mhz before it was injected into the predistorter. One of the tests to measure the quality of the transmitted signal is Adjacent Channel Power Rejection (ACPR). Due to the power amplifier’s non-linearity, there is spectral regrowth. The leakage of this power to the adjacent channel will cause interference to the adjacent channel. There are strict regulatory restrictions on this leakage of the power. Measuring the ACPR is indication of the linearity of the power amplifier. Page 71 Figure 4.9 Frequency spectrum at the input of the power amplifier (Before Linearization) Figure 4.10 Frequency spectrum at the ouptut of the power amplifier (Before Linearization) Page 72 Figure 4.11 Frequency spectrum at the input of the power amplifier (After Linearization) Figure 4.12 Frequency spectrum at the output of the power amplifier (After Linearization) Page 73 Figures 4.9 and 4.10 shows the input and output of the power amplifier before linearization respectively. At output of the power amplifier, there was a 20dB attenuator. Figure 4.11 and 4.12 shows the input and output of the power amplifier respectively after the predistorter was added. Before linearization, the ACPR before linearization was 30.00dB. After linearization, the ACPR improves to 35.47dB. Therefore there was an improvement of 5.47dB. Shown also in the results, Figures 4.9 and 4.11, are the frequency spectrum at the input of the power amplifier before and after linearization. From the two frequency spectrums, the predistorter will generate additional third order frequency components as predicted in chapter 3. These extra frequency components will cancel the third order frequency components generated by the power amplifier. 4.2.4 IS95 In the final test for low-IF linearization, the input signal was generated base on the standard IS95. It is cellular standard used in US. It uses code division multiple access (CDMA). The input signal has a high peak-to-average of about 10dB. The modulation used in the standard is QPSK. The bandwidth of the signal is 1.25Mhz. The center frequency of the transmitted signal is 1.83Ghz. Page 74 4.13 IS95 signals (Before Linearization) 4.14 IS95 signals (After Linearization) Page 75 The frequency spectrum of the power amplifier before and after linearization is applied is shown in Figures 4.13 and 4.14. There is a 20dB attenuator at the output of the power amplifier to protect the inputs to the spectrum analyser. The ACPR before linearization is 36.18dB. After linearization, the ACPR improves to 38.9dB. There is improvement of 2.72dB only. Compared to the work in [30] which uses a 5th order complex analog polynomial, the results does not present significant improvement. But the results presented in [30] were obtained at an IF of 200Mhz using a Class A amplifier. The power amplifier that was used in our test, RF Micro Devices’s RF2161, is biased as a Class AB power amplifier operating at 1.83Ghz. It is actual power amplifier used and it generates higher levels of distortions compared to [30]. Adaptive linearization could be used to tune the coefficients of the predistorter [31] for optimum performance of the power amplifier due to environmental and stimulus change. But it is beyond the scope of current work. 4.3 Baseband analog predistortion The predistorter was then moved to the baseband level after the digital to analogue (DAC) converter. At this position of the transmitter chain, the predistorter could potentially perform better than IF. The design of predistorter will be simpler as the bandwidth requirements are lower. Also there is a trend towards a zero-IF transmitter architecture design. In order words, there are no IF stage in the transmitter. After the DAC, I and Q channels will be modulated and upconverted to the desired RF frequency. Therefore the only place where the analogue predistorter could be used is at the baseband. Page 76 A modified two-tone test was first performed. Two tones are injected into both I and Q channels. The frequency spacing between the two tones is quite narrow (100Khz in this case). But the two tones are located at 1Mhz and 1.1Mhz. This is done so that it is possible to observe the harmonic and even order distortions generated by the predistorter. These harmonic and even order distortions could be filtered out when the predistorter is at the IF stage. But when the predistorter is placed at the baseband level, these distortions falls in band and could not be filtered out. These distortions will generate more distortions to the power amplifier. At the output of the RF power amplifier, it has four tones. The test set up is shown in Figure 4.15. Signal Source RF Amplifier Predistorter 90 degree Phase shifter 4.15 Test setup of baseband predistortion Spectrum Analyser Page 77 4.16 Overall output spectrum for baseband predistortion two-tone test (before linearization) 4.17 Zooming on the frequency spectrum around the two tone for baseband predistortion two-tone test (before linearization) Page 78 2nd order distortions 4.18 Overall output spectrum for baseband predistortion two-tone test (after linearization) 4.19 Zooming on the frequency spectrum around the two tones for baseband predistortion two-tone test (after linearization) Page 79 The results are shown in Figure 4.16 to 4.19. Figures 4.16 and 4.18 shows the whole frequency spectrum at the output of the power amplifier before and after linearization was applied respectively. There was a 20dB attenuator before the spectrum analyser. Figures 4.17 and 4.19 look at the frequency spectrum around the two tones on upper side band before and after linearization was applied respectively. From 4.17 and 4.19, the IMD3 was reduced from –45dBm to –65dBm. That is a reduction of 20dB in IMD3. It shows that the predistorter was reducing the third order distortions generated by the power amplifier. One interesting observation is that the IMD5 had also reduced by about 2dB after linearization was applied. However, comparing the overall frequency spectrum shown in Figures 4.16 and 4.18, there were extra frequency distortions at the output of the power amplifier after adding the predistorter. These extra frequency components were the second order distortions generated by the predistorter. The power levels of these second order distortions were around –32dBm. The second order distortions were due to the device mismatch, d.c offsets etc. These second order distortions generated by the predistorter could not be filtered out when the predistorter operates at the baseband. The work done L. Sundström and Timo Rahkonen [19][22][30] had not shown results when their complex analog predistorter is working at the baseband with a RF power amplifier. This is the first time these results are reported. Second order distortions could be reduced by paying close attention to matching of the transistors in analog multipliers. If the analog multipliers were mismatched, second order distortions will appear at the output of the predistorter. It is possible to reduce the second order distortions but not entirely eliminate it. This is because the matching of the transistor is partly process dependant and the wafer plant could not guarantee perfect matching. Page 80 4.4 Analog predistortion for Radio Over Fiber System (ROF) The predistorter was then used to linearize a non-linear optical system. There is currently active research to transmit radio signals over optical fiber. Transmitting radio signals over optical fiber has the potential to reduce the overall costs of the installation of cellular systems [32]. In the optical system, it consists of the electricalto-optical circuits, optical laser, photo detector, optical-to-electrical-circuits etc. The system exhibited characteristics similar to the power amplifier. When two tones were send into the system, the output seen from the spectrum analyser has 3rd order intermodulation distortions. Therefore the predistorter was used to linearize the optical system. The test set up is shown in Figure 4.20. Modulator Baseband Signal Source Optical System Predistorter RF Input Laser Diode Fibre Optics Spectrum Analyser RF Output Photo Detector Figure 4.20 Test Setup using predistorter in Radio Over Fiber system The same modified two-tones test used in Section 4.2 was used in this test. The transmitted RF frequency is 2.5Ghz. The two tones injected into the I and Q channel were 1.45Mhz and 1.55Mhz with a frequency spacing of 100khz apart. The results are shown in Figures 4.19 to 4.22. Page 81 4.21 Overall output spectrum for ROF predistortion two-tones test (before linearization) 4.22 Zooming on the frequency spectrum around the two tones for ROF predistortion two-tones test (before linearization) Page 82 2nd order distortions 4.23 Overall output spectrum for ROF predistortion two-tones test (after linearization) 4.24 Zooming on the frequency spectrum around the two tones for ROF predistortion two-tones test (after linearization) Page 83 The results in Figures 4.21 and 4.23 shows overall spectrum at the output of the ROF system. Comparing the two figures, there were additional frequency components generated by the predistorter. This was expected as stated in previous section 4.2. These distortions were the second order distortions generated by the predistorter. The power levels of these second order distortions were around –45dBm. Looking specifically at the two tones, shown in Figures 4.22 and 4.24, the IMD3 generated was reduced from –51dBm to –67dBm. It was a reduction of 16dB due to the predistorter. This demonstrates that the predistorter is able to reduce the distortions generated by the ROF system. The same two-tones test was repeated for different input power level. The distortions caused by the IMD3 were recorded before and after the predistorter was added. The output power was normalised. The results are shown in Figure 4.25. 0 Output Power of 2 Tones -10 Before Lineaization(IMD3) After Linearization(IMD3) -30 -40 -50 -60 -70 Input Power(dbm) Figure 4.25 Two-tones test for ROF system 0 -1 -2 -3 -4 -5 -6 -7 -8 -9 -10 -11 -80 -12 Output Power(dbm) -20 Page 84 From the results, the predistorter is able to reduce the distortions such that the power level of the IMD3 is below -60dBm. This is a significant reduction in IMD3 with the predistorter. There is only a single input power point, at -9dBm, that the predistorter is unable to decrease the IMD3. It might be due to some other anomalies operating in either the laser diode or photodiode that is not present in the power amplifier. The test was repeated again but instead of two tones a multi-carrier modulated signal was used as the input. The frequencies of the sub-carriers were carefully selected so the frequencies of each sub-carrier at the baseband must not coincide with its 2nd order distortions. The test setup was the same as two-tone test. The center carrier frequency is 2.5Ghz. There were five sub-carrier with the center carrier switched off and each was modulated with QPSK. The sub-carrier frequency spacing is 100khz and total bandwidth is 500khz. The results are shown in Figures 4.24 and 4.25. The total spectrum had a low and upper frequency side band similar to the overall output spectrum for the two-tones test. Figures 4.26 and 4.27 shows only the lower side band. Page 85 Out of Band Distortions Out of Band Distortions 4.26 Multi-Carrier Test for ROF system(Before Linearization) Out of Band Distortions Out of Band Distortions 4.27 Multi-Carrier Test for ROF system(After Linearization) Page 86 From the results shown in Figures 4.26 and 4.27, the power level of the center tone was reduced from –34.72dBm to –41.11dBm. The filling up of the center switched off carrier gives an indication of the distortion caused by the ROF system. It shows that the predistorter is able to reduce the distortions by 6.39dB. Another observation was that the out of band distortions were also reduced. In one of the out of band distortions, pointed by an arrow in Figures 4.24 and 4.25, the power level of the distortion drops from –37.5dBm to -43.75dBm. That is a reduction of 6.25dB. The distortion levels of the most serious distortions had decreased after linearization. In this series of tests using the ROF system, it shows that the predistorter could be extended to be use in the ROF system. The predistorter could reduce the IMD3 caused by the ROF systems. Chapter 5 Conclusions The power amplifier is a critical component in the transceiver. The power amplifiers suffers from both amplitude and phase distortions. It could be modelled using a complex odd order polynomial. However, the third order distortion is the most serious distortion generated by the power amplifier. This is even more dominant in a multicarrier system. In order to properly give a qualitative measure of the linearity of the power amplifier, different tests are introduced such as the two-tone test, Noise Power Ratio (NPR), Adjacent Power Rejection Ratio (ACPR). To improve the linearity of the power amplifier, three different general methods were mentioned, the Cartesian feedback, feedfoward and predistortion. In this thesis, the work was presented on linearizing the power amplifier using predistortion techniques. The predistorter could be implemented at different stages in Page 88 the transmitter chain. The predistorter implemented was a third order analog complex predistorter that could operate in the baseband and low-IF reducing the third order distortions from the power amplifier. One of the main blocks in the predistorter is the analog multiplier. An improved analog multiplier was introduced. Addition operation could be done by tying the outputs of two multipliers together. The load of the multiplier is diode connected MOS. It resistance is increased using positive feedback. The blocks of the predistorter are the transconductor, transimpedance cells and output buffers. It was fabricated in 0.8µm SiGe BiCMOS. In the tests for the predistorter chip, an actual RF power amplifier was used. In the two-tone test at low-IF, the predistorter had been able to reduce the third order intermodulation distortion significantly. Different test signals such as multi-carrier, OFDM had been used to inject into the predistorter. Using different metrics for the linearity of the power amplifier, such as NPR and ACPR, the predistorter had been shown to reduce the distortions caused by the power amplifier. In the baseband predistorter, the predistorter was shown to reduce the distortions caused by the power amplifier. However, due to the unwanted distortions generated by the predistorter, second order distortions could be observed at the output of the power amplifier. The predistorter was extended to be use in the Radio Over Fiber system. The characteristic of the system is similar to the power amplifier. In the testing, the predistorter was shown to reduce the distortions caused by the system. Page 89 Therefore, the third order analog complex predistorter is able to reduce the distortions of the power amplifier, improving its linearity. This would allow the power amplifier to operate at higher power efficiency. The use of the predistorter had been extended to ROF system. This raises the possibility of using the predistorter in other areas. Bibliography [1] Behzad Razavi, “RF Microelectronics”, Prentice Hall, 1st edition, 1997 [2] Raab, F.H.; Asbeck, P.; Cripps, S.; Kenington, P.B.; Popovic, Z.B.; Pothecary N.; Sevic, J.F.; Sokal, N.O, “Power amplifiers and transmitters for RF and microwave”, IEEE Trans. on Microwave Theory and Techniques, Vol. 50 Issue 3, Mar 2002, pp. 814 -826 [3] Chris Toumazou and George Moschytz, “Trade-Offs in Analog Circuit Design”, Kluwer Academic Publishers ,2002 [4] RF Micro Devices, Part No. RF2161, www.rfmd.com [5] Raytheon, Part No. RMPA5251-251, www.raytheonrf.com [6] Nathan O. Sakal and Alan D. Sokal, “Class E – A New Class of HighEfficiency Tuned single-Ended Switching Power Amplifiers”, IEEE Journal of Solid State Circuits, Vol. 10, pp. 168-175, June 1975 [7] Peter B. Kenington, “High Linearity RF Amplifier Design”, Artech Hous,2000 [8] Steve C. Cripps, “RF Power Amplifiers for Wireless Communications”, Artech House,1999 Page 91 [9] Joel H. K. Vuolei, Timo Rahkonen and Jani P. A. Manninen, “Measurements Technique for Characterizing Memory Effects in RF Power Amplifiers”, IEEE Trans. on Microwave Theory and Tecniques, Vol. 49, No. 8, August 2001, pp. 1383-1389 [10] Joel Vuolei, Timo Rahkonen and Jani Manninen, “Canceling the memory effects in RF Power Amplifier”, ISCAS 2001, 6-9 May 2001, pp. 57 -60 [11] Steve C. Cripps, “Advanced Techniques in RF Power Amplifier Design”, Artech House, 2002 [12] Saleh, A. A. M., “Frequency-independent and frequency-dependant non-linear models of TWT amplifiers”, IEEE Trans. on Communications, Vol. COM-29, November 1981, pp. 1715-1720 [13] Agilent Application Note, AN 1311, “Understanding CDMA Measurements for Base Stations and Their Components”, Agilent Tehnologies, www.agilent.com [14] Back, H. S., US Patent no. 1,686,792, 9th October 1928 [15] Mats Johansson and Thomas Mattsson, “Transmitter Linearization using Cartesian Feedback for Linear TDMA Modulation”, IEEE Vehicular Technology Conference, 19-22 May 1991, pp. 439 –444 Page 92 [16] Nick Pothecary, “Feedfoward Linear Power Amplifiers”, Artech House, 1999 [17] James K. Cavers, “Adaptation Behavior of a Feedfoward Amplifier Linearizer”, IEEE Trans. on Vehicular Technology, Vol. 44, No. 1, Feb. 1995, pp. 31-40 [18] Tri T. Ha, “Digital Satellite Communications”, McGraw Hill, 1986 [19] E. Westesson, L. Sundström, “A complex polynomial predistorter chip in CMOS for baseband or IF linearization of RF power amplifier”, ISCAS '99, Proceedings of the 1999 IEEE International Symposium, vol. 1, Jul 1999 [20] Natasa Males-Ilic, Bratislav Milovanoic, Djuradj Budimir, “Linearization Technique for reducing Third- ad Fifth Order Intermodulation Distortion Products in Multichannel Amplifier”, 33rd European Microwave Conference, Munich 2003. [21] James K. Cavers, “Amplifier Linearization Using a Digital Predistorter with Fast Adptation and Low Memory Requirements”, IEEE Trans. On Vehicular Technology, vol 39, no. 4, pp. 374-382, Nov. 1990 [22] Timo Rahkonen, Tapio Kankaala, Marko Neitola and Antti Heiskanen, “Using Analog Predistortion for Linearizing Class A-C Power Amplifiers”, Analog Integrated Circuits and Signal Processing, 22, 1999, pp. 31-39 Page 93 [23] C. Toumazou, F.J. Lidgey & D.G. Haigh, “Analogue IC design: the currentmode approach”, Institution of Electrical Engineers, 1993 [24] B. Gilbert, “A precision four-quadrant multiplier with subnanosecond response,” IEEE Journal of Solid State Circuits, Vol. SC-3, pp. 353-365, Dec 1968 [25] Gunhee Han and Edgar Sánchex-Sinencio, “CMOS Transconductance Multipliers: A Tutorial”, IEEE Trans. On Cricuits and Systems II: Analog and Digital Signal Processing, vol 45, No 12, Dec 1998, pp. 1550-1563 [26] Behzad Razavi, “Design of Analog CMOS Integrated Circuits”, McGraw Hill, 1st Edition, 2000 [27] Mezyad Amourah and Randall Geiger, “A High Gain Strategy with positivefeedback gain enhancement Technique”, ISCAS 2001, The 2001 IEEE International Symposium, vol. 1, 6-9 May 2001 [28] Cadence Design Systems, “www.cadence.com” [29] Christopher Saint and Judy Saint, “IC Mask Design, Essential Layout Techniques”, McGraw Hill, 1st Edition, 2002 Page 94 [30] WESTESSON E and SUNDSTRÖM L.: "Low Power Complex Polynomial Predistorter Circuit in CMOS for RF PA Linearization", Proceedings of 27th Europe Solid State Circuits Conf. 2001 [31] Allen Katz, “Linearization: Reducing distortion in Power Amplifier”, IEEE Microwave Magazine, Dec 2001, pp.37-49 [32] Hamed Al-Raweshidy and Shozo Komaki, “Radio Over Fiber Technologies for Mobile Communications Networks”, Artech House, 1st Edition, 2002 Appendix Netlist of Predistorter Chip // Generated for: spectre // Generated on: Dec 13 15:28:00 2004 // Design library name: pd3 // Design cell name: pd_top1 // Design view name: schematic simulator lang=spectre global 0 include "/opt/ic/446.100.111.8/tools.sun4v/dfII/samples/artist/ahdlLib/quantity.spectre" include "/opt/process/AMS_3.40_CDS/spectre/byr/mcparams.scs" include "/opt/process/AMS_3.40_CDS/spectre/byr/cmos53.scs" section=cmostm include "/opt/process/AMS_3.40_CDS/spectre/byr/res.scs" section=restm include "/opt/process/AMS_3.40_CDS/spectre/byr/cap.scs" section=captm include "/opt/process/AMS_3.40_CDS/spectre/byr/vbic.scs" section=biptm // Library name: cartesian // Cell name: INV_PD // View name: schematic subckt INV_PD IN OUT vdd vss vtie I4 (OUT IN vss vtie) modn w=2.4u l=0.8u as=5.52e-12 ad=5.52e-12 ps=7u \ pd=7u nrd=0.541667 nrs=0.541667 ng=1 I3 (OUT IN vdd vdd) modp w=4.8u l=0.8u as=1.104e-11 ad=1.104e-11 \ ps=9.4u pd=9.4u nrd=0.270833 nrs=0.270833 ng=1 ends INV_PD // End of subcircuit definition. // Library name: cartesian // Cell name: npnx10_bandgap // View name: schematic subckt npnx10_bandgap B C E SUB I8 (C B E SUB) npn111 area=2 m=1 I9 (C B E SUB) npn111 area=2 m=1 I10 (C B E SUB) npn111 area=2 m=1 I7 (C B E SUB) npn111 area=2 m=1 I6 (C B E SUB) npn111 area=2 m=1 I5 (C B E SUB) npn111 area=2 m=1 I3 (C B E SUB) npn111 area=2 m=1 I4 (C B E SUB) npn111 area=2 m=1 I2 (C B E SUB) npn111 area=2 m=1 Page 96 I1 (C B E SUB) npn111 area=2 m=1 ends npnx10_bandgap // End of subcircuit definition. // Library name: SCHEMA // Cell name: cpolybr3 // View name: schematic subckt cpolybr3 PLUS MINUS REF parameters area=100p perimeter=40u np=1 csub=1f rsub=1 rp1=1 rp2=1 CP1B (top bottom) cpolyb area=area perimeter=perimeter m=np C11 (bottom int3) capacitor c=csub m=np R12 (int3 REF) resistor r=rsub m=np RP1 (bottom MINUS) resistor r=rp1 m=np RPB (PLUS top) resistor r=rp2 m=np ends cpolybr3 // End of subcircuit definition. // Library name: cartesian // Cell name: bandgap // View name: schematic subckt bandgap PD ibg_1mI_0 ibg_1mQ_0 ibg_2mI_0 ibg_2mQ_0 ibg_50uI_0 \ ibg_50uI_1 ibg_50uQ_0 ibg_50uQ_1 vbg_fb vbg_out1 vbg_out2 vdda \ vssa vtie I1 (PD PDb vdda vssa vtie) INV_PD Q2 (net451 net449 net260 vtie) npnx10_bandgap Q15 (vbg_fb net198 net266 vtie) npnx10_bandgap C0 (net406 vssa vtie) cpolybr3 area=5.61516e-09 perimeter=305.802u \ np=1 csub=462.823f rsub=100 rp1=12.0278 rp2=47.2345 C2 (ibg_i vssa vtie) cpolybr3 area=5.61516e-09 perimeter=305.802u np=1 \ csub=462.823f rsub=100 rp1=12.0278 rp2=47.2345 C1 (net190 vssa vtie) cpolybr3 area=1.11454e-09 perimeter=136.301u \ np=1 csub=113.897f rsub=100 rp1=6.14195 rp2=47.1873 I120 (net215 PD vssa vtie) modn w=2u l=0.8u as=4.6e-12 ad=4.6e-12 \ ps=6.6u pd=6.6u nrd=0.65 nrs=0.65 ng=1 I121 (vbg_fb PD vssa vtie) modn w=2u l=0.8u as=4.6e-12 ad=4.6e-12 \ ps=6.6u pd=6.6u nrd=0.65 nrs=0.65 ng=1 M1 (net222 net222 vssa vtie) modn w=2u l=120u as=4.6e-12 ad=4.6e-12 \ ps=6.6u pd=6.6u nrd=0.65 nrs=0.65 ng=1 M19 (BG_GEN PD vssa vtie) modn w=2u l=0.8u as=4.6e-12 ad=4.6e-12 \ ps=6.6u pd=6.6u nrd=0.65 nrs=0.65 ng=1 M9 (net231 net359 net232 vtie) modn w=80u l=2u as=1.84e-10 ad=1.84e-10 \ ps=84.6u pd=84.6u nrd=0.01625 nrs=0.01625 ng=1 M10 (net332 BG_GEN net232 vtie) modn w=80u l=2u as=1.84e-10 \ ad=1.84e-10 ps=84.6u pd=84.6u nrd=0.01625 nrs=0.01625 ng=1 M20 (ibg_out1 BG_GEN vbg_out1 vtie) modn w=200u l=2u as=4.6e-10 \ ad=4.6e-10 ps=204.6u pd=204.6u nrd=0.0065 nrs=0.0065 ng=1 RD1 (vtie net210) rpoly2 w=6u l=25.8u m=1 R15 (vtie net200) rpoly2 w=6u l=25.8u m=1 R26 (net248 vssa) rpoly2 w=6u l=77.4u m=1 R27 (net248 vssa) rpoly2 w=6u l=77.4u m=1 R23 (net250 vssa) rpoly2 w=6u l=77.4u m=1 R24 (net248 vssa) rpoly2 w=6u l=77.4u m=1 R29 (vtie net509) rpoly2 w=6u l=77.4u m=1 R30 (vtie net510) rpoly2 w=6u l=77.4u m=1 R28 (ibg_i vssa) rpoly2 w=6u l=1856.000u m=1 R25 (net248 vssa) rpoly2 w=6u l=77.4u m=1 Page 97 R2 (net258 vssa) rpoly2 w=6u l=309.4u m=1 R1 (net260 vssa) rpoly2 w=6u l=102.9u m=1 R22 (net252 vssa) rpoly2 w=6u l=77.4u m=1 R5 (BG_STAB net190) rpoly2 w=6u l=580.00000u m=1 R4 (BG_COM vssa) rpoly2 w=6u l=313.2u m=1 R3 (net266 BG_COM) rpoly2 w=6u l=102.9u m=1 I142 (ibg_out1 ibg_out1 vdda vdda) modp w=50u l=2u as=1.15e-10 \ ad=1.15e-10 ps=54.6u pd=54.6u nrd=0.026 nrs=0.026 ng=1 I161 (ibg_i ibg_out1 vdda vdda) modp w=50u l=2u as=1.15e-10 \ ad=1.15e-10 ps=54.6u pd=54.6u nrd=0.026 nrs=0.026 ng=1 I173 (ibg_out2 ibg_out2 vdda vdda) modp w=500u l=2u as=1.15e-09 \ ad=1.15e-09 ps=504.6u pd=504.6u nrd=0.0026 nrs=0.0026 ng=1 I168 (ibg_2mQ_0 ibg_out2 vdda vdda) modp w=500u l=2u as=1.15e-09 \ ad=6.5e-10 ps=504.6u pd=2.6u nrd=0.0026 nrs=0.0026 ng=2 I175 (ibg_out2 PDb vdda vdda) modp w=40u l=0.8u as=9.2e-11 ad=9.2e-11 \ ps=44.6u pd=44.6u nrd=0.0325 nrs=0.0325 ng=1 I165 (net390 net390 vdda vdda) modp w=100u l=2u as=2.3e-10 ad=2.3e-10 \ ps=104.6u pd=104.6u nrd=0.013 nrs=0.013 ng=1 I199 (ibg_50uI_0 ibg_out1 vdda vdda) modp w=50u l=2u as=1.15e-10 \ ad=1.15e-10 ps=54.6u pd=54.6u nrd=0.026 nrs=0.026 ng=1 I200 (ibg_50uQ_0 ibg_out1 vdda vdda) modp w=50u l=2u as=1.15e-10 \ ad=1.15e-10 ps=54.6u pd=54.6u nrd=0.026 nrs=0.026 ng=1 I163 (net406 net390 vdda vdda) modp w=100u l=2u as=2.3e-10 ad=2.3e-10 \ ps=104.6u pd=104.6u nrd=0.013 nrs=0.013 ng=1 I167 (ibg_50uQ_1 ibg_out1 vdda vdda) modp w=50u l=2u as=1.15e-10 \ ad=1.15e-10 ps=54.6u pd=54.6u nrd=0.026 nrs=0.026 ng=1 I164 (net390 PDb vdda vdda) modp w=4u l=0.8u as=9.2e-12 ad=9.2e-12 \ ps=8.6u pd=8.6u nrd=0.325 nrs=0.325 ng=1 I181 (net435 ibias_out vdda vdda) modp w=25u l=2u as=5.75e-11 \ ad=5.75e-11 ps=29.6u pd=29.6u nrd=0.052 nrs=0.052 ng=1 M4 (net331 PD vdda vdda) modp w=2u l=1u as=4.6e-12 ad=4.6e-12 ps=6.6u \ pd=6.6u nrd=0.65 nrs=0.65 ng=1 M3 (net215 net222 net331 net331) modp w=5u l=1u as=1.15e-11 \ ad=1.15e-11 ps=9.6u pd=9.6u nrd=0.26 nrs=0.26 ng=1 I197 (ibg_1mI_0 ibg_out2 vdda vdda) modp w=500u l=2u as=1.15e-09 \ ad=1.15e-09 ps=504.6u pd=504.6u nrd=0.0026 nrs=0.0026 ng=1 I198 (ibg_1mQ_0 ibg_out2 vdda vdda) modp w=500u l=2u as=1.15e-09 \ ad=1.15e-09 ps=504.6u pd=504.6u nrd=0.0026 nrs=0.0026 ng=1 M2 (net222 net332 vdda vdda) modp w=50u l=2u as=1.15e-10 ad=1.15e-10 \ ps=54.6u pd=54.6u nrd=0.026 nrs=0.026 ng=1 M11 (net231 net231 vdda vdda) modp w=10u l=2u as=2.3e-11 ad=2.3e-11 \ ps=14.6u pd=14.6u nrd=0.13 nrs=0.13 ng=1 M8 (net332 net332 vdda vdda) modp w=10u l=2u as=2.3e-11 ad=2.3e-11 \ ps=14.6u pd=14.6u nrd=0.13 nrs=0.13 ng=1 I171 (net626 net546 vdda vdda) modp w=25u l=2u as=3.60714e-11 \ ad=3.60714e-11 ps=6.45714u pd=6.45714u nrd=0.052 nrs=0.052 ng=7 M5 (net215 ibias_out vdda vdda) modp w=25u l=2u as=5.75e-11 \ ad=5.75e-11 ps=29.6u pd=29.6u nrd=0.052 nrs=0.052 ng=1 I193 (ibg_2mI_0 ibg_out2 vdda vdda) modp w=500u l=2u as=1.15e-09 \ ad=6.5e-10 ps=504.6u pd=2.6u nrd=0.0026 nrs=0.0026 ng=2 I196 (ibg_50uI_1 ibg_out1 vdda vdda) modp w=50u l=2u as=1.15e-10 \ ad=1.15e-10 ps=54.6u pd=54.6u nrd=0.026 nrs=0.026 ng=1 M22 (ibg_out1 PDb vdda vdda) modp w=2u l=0.8u as=4.6e-12 ad=4.6e-12 \ ps=6.6u pd=6.6u nrd=0.65 nrs=0.65 ng=1 M13 (ibias_out PDb vdda vdda) modp w=2u l=0.8u as=4.6e-12 ad=4.6e-12 \ ps=6.6u pd=6.6u nrd=0.65 nrs=0.65 ng=1 M7 (net459 net459 net359 net359) modp w=15u l=1u as=3.45e-11 \ Page 98 ad=3.45e-11 ps=19.6u pd=19.6u nrd=0.0866667 nrs=0.0866667 ng=1 M6 (net359 ibias_out vdda vdda) modp w=5u l=2u as=1.15e-11 ad=1.15e-11 \ ps=9.6u pd=9.6u nrd=0.26 nrs=0.26 ng=1 M17 (BG_STAB net231 vdda vdda) modp w=20u l=2u as=4.6e-11 ad=4.6e-11 \ ps=24.6u pd=24.6u nrd=0.065 nrs=0.065 ng=1 M12 (ibias_out ibias_out vdda vdda) modp w=25u l=2u as=5.75e-11 \ ad=5.75e-11 ps=29.6u pd=29.6u nrd=0.052 nrs=0.052 ng=1 M14 (BG_GEN ibias_out vdda vdda) modp w=25u l=2u as=4.3125e-11 \ ad=2.875e-11 ps=15.95u pd=2.3u nrd=0.052 nrs=0.052 ng=4 M18 (vssa BG_STAB BG_GEN BG_GEN) modp w=120u l=2u as=2.76e-10 \ ad=2.76e-10 ps=124.6u pd=124.6u nrd=0.0108333 nrs=0.0108333 ng=1 M16 (BG_STAB net198 BG_GEN BG_GEN) modp w=60u l=2u as=1.38e-10 \ ad=1.38e-10 ps=64.6u pd=64.6u nrd=0.0216667 nrs=0.0216667 ng=1 M15 (net198 net198 BG_GEN BG_GEN) modp w=60u l=2u as=1.38e-10 \ ad=1.38e-10 ps=64.6u pd=64.6u nrd=0.0216667 nrs=0.0216667 ng=1 Q3 (ibias_out net215 net449 vtie) npn111 area=2 m=1 Q16 (BG_STAB vbg_fb BG_COM vtie) npn111 area=2 m=1 I189 (net390 ibg_i net389 vtie) npn111 area=2 m=1 I177 (ibg_out2 net406 vbg_out2 vtie) npn111 area=2 m=1 I178 (net389 net433 net248 vtie) npn111 area=2 m=1 I176 (ibg_out2 net406 vbg_out2 vtie) npn111 area=2 m=1 I185 (net433 net433 net250 vtie) npn111 area=2 m=1 I180 (vdda net435 net433 vtie) npn111 area=2 m=1 I126 (net427 net203 net211 vtie) npn111 area=2 m=1 I127 (net431 net202 net201 vtie) npn111 area=2 m=1 I179 (net435 net433 net252 vtie) npn111 area=2 m=1 Q5 (net232 net451 net258 vtie) npn111 area=2 m=1 I128 (net443 net207 net212 vtie) npn111 area=2 m=1 I125 (net447 net205 net209 vtie) npn111 area=2 m=1 Q0 (net451 net449 vssa vtie) npn111 area=2 m=1 Q1 (net215 net215 net451 vtie) npn111 area=2 m=1 I190 (net406 vbg_out2 net389 vtie) npn111 area=2 m=1 Q4 (net459 net459 vssa vtie) npn111 area=2 m=1 ends bandgap // End of subcircuit definition. // Library name: pd3 // Cell name: output_buffer // View name: schematic subckt output_buffer Iin\+ Iin\- Vout\+ Vout\- Vref vdd vss vtie i_1mA I54 (Vout\- net051 vss vtie) npn112 area=4 m=1 I49 (Vout\+ net051 vss vtie) npn112 area=4 m=1 I48 (vdd net30 Vout\+ vtie) npn111 area=2 m=1 I51 (vdd i_1mA net051 vtie) npn111 area=2 m=1 I55 (vdd net031 Vout\- vtie) npn111 area=2 m=1 I50 (i_1mA net051 vss vtie) npn111 area=2 m=1 I13 (Iin\+ Iin\+ vss vtie) modn w=8u l=2u as=1.84e-11 ad=1.84e-11 \ ps=12.6u pd=12.6u nrd=0.1625 nrs=0.1625 ng=1 I14 (Iin\- Iin\- vss vtie) modn w=8u l=2u as=1.84e-11 ad=1.84e-11 \ ps=12.6u pd=12.6u nrd=0.1625 nrs=0.1625 ng=1 I16 (Iin\- Vref vdd vdd) modp w=65u l=2u as=1.495e-10 ad=1.495e-10 \ ps=69.6u pd=69.6u nrd=0.02 nrs=0.02 ng=1 I19 (vss Iin\+ net30 net30) modp w=20u l=2u as=4.6e-11 ad=4.6e-11 \ ps=24.6u pd=24.6u nrd=0.065 nrs=0.065 ng=1 I21 (net031 Vref vdd vdd) modp w=100u l=2u as=2.3e-10 ad=2.3e-10 \ ps=104.6u pd=104.6u nrd=0.013 nrs=0.013 ng=1 I22 (net30 Vref vdd vdd) modp w=100u l=2u as=2.3e-10 ad=2.3e-10 \ Page 99 ps=104.6u pd=104.6u nrd=0.013 nrs=0.013 ng=1 I20 (vss Iin\- net031 net031) modp w=20u l=2u as=4.6e-11 ad=4.6e-11 \ ps=24.6u pd=24.6u nrd=0.065 nrs=0.065 ng=1 I15 (Iin\+ Vref vdd vdd) modp w=65u l=2u as=1.495e-10 ad=1.495e-10 \ ps=69.6u pd=69.6u nrd=0.02 nrs=0.02 ng=1 ends output_buffer // End of subcircuit definition. // Library name: pd3 // Cell name: balanced_diff_current // View name: schematic subckt balanced_diff_current Iin\+ Iin\- Iout\+ Iout\- vdd vss vtie I38 (net70 net70 vdd vdd) modp w=50u l=2u as=1.15e-10 ad=1.15e-10 \ ps=54.6u pd=54.6u nrd=0.026 nrs=0.026 ng=1 I31 (Iout\- net70 vdd vdd) modp w=50u l=2u as=1.15e-10 ad=1.15e-10 \ ps=54.6u pd=54.6u nrd=0.026 nrs=0.026 ng=1 I5 (Iout\+ net82 vdd vdd) modp w=50u l=2u as=1.15e-10 ad=1.15e-10 \ ps=54.6u pd=54.6u nrd=0.026 nrs=0.026 ng=1 I4 (net82 net82 vdd vdd) modp w=50u l=2u as=1.15e-10 ad=1.15e-10 \ ps=54.6u pd=54.6u nrd=0.026 nrs=0.026 ng=1 I3 (Iout\- Iin\+ vss vtie) modn w=25u l=2u as=5.75e-11 ad=5.75e-11 \ ps=29.6u pd=29.6u nrd=0.052 nrs=0.052 ng=1 I12 (net70 Iin\- vss vtie) modn w=25u l=2u as=5.75e-11 ad=5.75e-11 \ ps=29.6u pd=29.6u nrd=0.052 nrs=0.052 ng=1 I33 (Iout\+ Iin\- vss vtie) modn w=25u l=2u as=5.75e-11 ad=5.75e-11 \ ps=29.6u pd=29.6u nrd=0.052 nrs=0.052 ng=1 I2 (Iin\+ Iin\+ vss vtie) modn w=25u l=2u as=5.75e-11 ad=5.75e-11 \ ps=29.6u pd=29.6u nrd=0.052 nrs=0.052 ng=1 I1 (net82 Iin\+ vss vtie) modn w=25u l=2u as=5.75e-11 ad=5.75e-11 \ ps=29.6u pd=29.6u nrd=0.052 nrs=0.052 ng=1 I0 (Iin\- Iin\- vss vtie) modn w=25u l=2u as=5.75e-11 ad=5.75e-11 \ ps=29.6u pd=29.6u nrd=0.052 nrs=0.052 ng=1 ends balanced_diff_current // End of subcircuit definition. // Library name: pd3 // Cell name: pd_output_top // View name: schematic subckt pd_output_top Iin\+ Iin\- Vout\+ Vout\- Vref vdd vss vtie i_1mA I8 (net022 net021 Vout\+ Vout\- Vref vdd vss vtie i_1mA) output_buffer I6 (Iin\+ Iin\- net022 net021 vdd vss vtie) balanced_diff_current ends pd_output_top // End of subcircuit definition. // Library name: pd3 // Cell name: LinearRegion_MOS_Multiplier2_CoupledLoad // View name: schematic subckt LinearRegion_MOS_Multiplier2_CoupledLoad Vout\+ Vout\- Vref Vx1\+ \ Vx1\- Vx2\+ Vx2\- Vy1\+ Vy1\- Vy2\+ Vy2\- vdd vss vtie I69 (vss net0231 net0118 net0118) modp w=10u l=2u as=2.3e-11 \ ad=2.3e-11 ps=14.6u pd=14.6u nrd=0.13 nrs=0.13 ng=1 I77 (net0114 Vref vdd vdd) modp w=10u l=2u as=2.3e-11 ad=2.3e-11 \ ps=14.6u pd=14.6u nrd=0.13 nrs=0.13 ng=1 I78 (vss net096 net0114 net0114) modp w=10u l=2u as=2.3e-11 ad=2.3e-11 \ ps=14.6u pd=14.6u nrd=0.13 nrs=0.13 ng=1 I75 (net0147 Vref vdd vdd) modp w=20u l=2u as=4.6e-11 ad=4.6e-11 \ ps=24.6u pd=24.6u nrd=0.065 nrs=0.065 ng=1 Page 100 I41 (V\+ V\- vdd vdd) modp w=35u l=2u as=8.05e-11 ad=8.05e-11 ps=39.6u \ pd=39.6u nrd=0.0371429 nrs=0.0371429 ng=1 I39 (V\- V\+ vdd vdd) modp w=35u l=2u as=8.05e-11 ad=8.05e-11 ps=39.6u \ pd=39.6u nrd=0.0371429 nrs=0.0371429 ng=1 I70 (net0118 Vref vdd vdd) modp w=10u l=2u as=2.3e-11 ad=2.3e-11 \ ps=14.6u pd=14.6u nrd=0.13 nrs=0.13 ng=1 I44 (net054 Vref vdd vdd) modp w=50u l=2u as=1.15e-10 ad=1.15e-10 \ ps=54.6u pd=54.6u nrd=0.026 nrs=0.026 ng=1 I10 (V\+ V\+ vdd vdd) modp w=50u l=2u as=1.15e-10 ad=1.15e-10 ps=54.6u \ pd=54.6u nrd=0.026 nrs=0.026 ng=1 I11 (V\- V\- vdd vdd) modp w=50u l=2u as=1.15e-10 ad=1.15e-10 ps=54.6u \ pd=54.6u nrd=0.026 nrs=0.026 ng=1 I88 (net0147 net0172 vss vtie) npn111 area=2 m=1 I90 (Vout\+ net0172 vss vtie) npn111 area=2 m=1 I91 (Vout\- net0172 vss vtie) npn111 area=2 m=1 I92 (vdd net0147 net0172 vtie) npn111 area=2 m=1 I30 (V\+ Vy2\- net0117 vtie) npn111 area=2 m=1 I31 (V\- Vy2\- net0113 vtie) npn111 area=2 m=1 I32 (V\- Vy2\+ net0109 vtie) npn111 area=2 m=1 I33 (V\+ Vy2\+ net0105 vtie) npn111 area=2 m=1 I19 (vdd net054 net060 vtie) npn111 area=2 m=1 I16 (net054 net060 vss vtie) npn111 area=2 m=1 I14 (net058 net060 vss vtie) npn111 area=2 m=1 I5 (V\+ Vy1\- net26 vtie) npn111 area=2 m=1 I4 (V\- Vy1\- net30 vtie) npn111 area=2 m=1 I2 (V\- Vy1\+ net34 vtie) npn111 area=2 m=1 I1 (V\+ Vy1\+ net38 vtie) npn111 area=2 m=1 I79 (vdd net0114 Vout\- vtie) modn w=10u l=2u as=2.3e-11 ad=2.3e-11 \ ps=14.6u pd=14.6u nrd=0.13 nrs=0.13 ng=1 I82 (net0231 net0241 vss vtie) modn w=8u l=2u as=1.84e-11 ad=1.84e-11 \ ps=12.6u pd=12.6u nrd=0.1625 nrs=0.1625 ng=1 I71 (vdd net0118 Vout\+ vtie) modn w=10u l=2u as=2.3e-11 ad=2.3e-11 \ ps=14.6u pd=14.6u nrd=0.13 nrs=0.13 ng=1 I83 (net096 net0245 vss vtie) modn w=8u l=2u as=1.84e-11 ad=1.84e-11 \ ps=12.6u pd=12.6u nrd=0.1625 nrs=0.1625 ng=1 I84 (vdd vdd net096 vtie) modn w=4u l=2u as=9.2e-12 ad=9.2e-12 ps=8.6u \ pd=8.6u nrd=0.325 nrs=0.325 ng=1 I43 (vdd vdd net0241 vtie) modn w=3u l=2u as=6.9e-12 ad=6.9e-12 \ ps=7.6u pd=7.6u nrd=0.433333 nrs=0.433333 ng=1 I34 (net0117 Vx2\- vss vtie) modn w=4.5u l=2u as=1.035e-11 \ ad=1.035e-11 ps=9.1u pd=9.1u nrd=0.288889 nrs=0.288889 ng=1 I35 (net0113 Vx2\+ vss vtie) modn w=4.5u l=2u as=1.035e-11 \ ad=1.035e-11 ps=9.1u pd=9.1u nrd=0.288889 nrs=0.288889 ng=1 I36 (net0109 Vx2\- vss vtie) modn w=4.5u l=2u as=1.035e-11 \ ad=1.035e-11 ps=9.1u pd=9.1u nrd=0.288889 nrs=0.288889 ng=1 I37 (net0105 Vx2\+ vss vtie) modn w=4.5u l=2u as=1.035e-11 \ ad=1.035e-11 ps=9.1u pd=9.1u nrd=0.288889 nrs=0.288889 ng=1 I42 (vdd vdd net0245 vtie) modn w=3u l=2u as=6.9e-12 ad=6.9e-12 \ ps=7.6u pd=7.6u nrd=0.433333 nrs=0.433333 ng=1 I81 (vdd vdd net0231 vtie) modn w=4u l=2u as=9.2e-12 ad=9.2e-12 \ ps=8.6u pd=8.6u nrd=0.325 nrs=0.325 ng=1 I20 (net0241 V\+ net058 vtie) modn w=10u l=2u as=2.3e-11 ad=2.3e-11 \ ps=14.6u pd=14.6u nrd=0.13 nrs=0.13 ng=1 I21 (net0245 V\- net058 vtie) modn w=10u l=2u as=2.3e-11 ad=2.3e-11 \ ps=14.6u pd=14.6u nrd=0.13 nrs=0.13 ng=1 I7 (net26 Vx1\- vss vtie) modn w=4.5u l=2u as=1.035e-11 ad=1.035e-11 \ ps=9.1u pd=9.1u nrd=0.288889 nrs=0.288889 ng=1 Page 101 I6 (net30 Vx1\+ vss vtie) modn w=4.5u l=2u as=1.035e-11 ad=1.035e-11 \ ps=9.1u pd=9.1u nrd=0.288889 nrs=0.288889 ng=1 I3 (net34 Vx1\- vss vtie) modn w=4.5u l=2u as=1.035e-11 ad=1.035e-11 \ ps=9.1u pd=9.1u nrd=0.288889 nrs=0.288889 ng=1 I0 (net38 Vx1\+ vss vtie) modn w=4.5u l=2u as=1.035e-11 ad=1.035e-11 \ ps=9.1u pd=9.1u nrd=0.288889 nrs=0.288889 ng=1 ends LinearRegion_MOS_Multiplier2_CoupledLoad // End of subcircuit definition. // Library name: pd3 // Cell name: transconductor1_test // View name: schematic subckt transconductor1_test I\+ I\- Vin\+ Vin\- Vref vdd vss vtie I32 (net27 net057 vss vtie) npn112 area=4 m=1 I34 (vdd net051 net057 vtie) npn111 area=2 m=1 I33 (net051 net057 vss vtie) npn111 area=2 m=1 I31 (net46 net057 vss vtie) npn111 area=2 m=1 I38 (I\+ net093 vdd vdd) modp w=37.5u l=2u as=8.625e-11 ad=8.625e-11 \ ps=42.1u pd=42.1u nrd=0.0346667 nrs=0.0346667 ng=1 I39 (I\- net081 vdd vdd) modp w=37.5u l=2u as=8.625e-11 ad=8.625e-11 \ ps=42.1u pd=42.1u nrd=0.0346667 nrs=0.0346667 ng=1 I37 (net051 Vref vdd vdd) modp w=50u l=2u as=1.15e-10 ad=1.15e-10 \ ps=54.6u pd=54.6u nrd=0.026 nrs=0.026 ng=1 I19 (net093 net093 vdd vdd) modp w=50u l=2u as=1.15e-10 ad=1.15e-10 \ ps=54.6u pd=54.6u nrd=0.026 nrs=0.026 ng=1 I20 (net081 net081 vdd vdd) modp w=50u l=2u as=1.15e-10 ad=1.15e-10 \ ps=54.6u pd=54.6u nrd=0.026 nrs=0.026 ng=1 I11 (net081 Vin\+ net46 vtie) modn w=7u l=2u as=1.61e-11 ad=1.61e-11 \ ps=11.6u pd=11.6u nrd=0.185714 nrs=0.185714 ng=1 I12 (net093 Vin\- net46 vtie) modn w=7u l=2u as=1.61e-11 ad=1.61e-11 \ ps=11.6u pd=11.6u nrd=0.185714 nrs=0.185714 ng=1 I2 (net081 Vin\- net27 vtie) modn w=10u l=2u as=2.3e-11 ad=2.3e-11 \ ps=14.6u pd=14.6u nrd=0.13 nrs=0.13 ng=1 I0 (net093 Vin\+ net27 vtie) modn w=10u l=2u as=2.3e-11 ad=2.3e-11 \ ps=14.6u pd=14.6u nrd=0.13 nrs=0.13 ng=1 ends transconductor1_test // End of subcircuit definition. // Library name: pd3 // Cell name: Basic_Multiplier_Biasing // View name: schematic subckt Basic_Multiplier_Biasing Iref Vref vdd vss vtie I12 (net043 net55 vss vtie) modn w=11u l=2u as=2.53e-11 ad=2.53e-11 \ ps=15.6u pd=15.6u nrd=0.118182 nrs=0.118182 ng=1 I26 (Iref Iref net55 vtie) modn w=50u l=2u as=1.15e-10 ad=1.15e-10 \ ps=54.6u pd=54.6u nrd=0.026 nrs=0.026 ng=1 I0 (net55 net55 vss vtie) modn w=50u l=2u as=1.15e-10 ad=1.15e-10 \ ps=54.6u pd=54.6u nrd=0.026 nrs=0.026 ng=1 I27 (Vref Iref net043 vtie) modn w=11u l=2u as=2.53e-11 ad=2.53e-11 \ ps=15.6u pd=15.6u nrd=0.118182 nrs=0.118182 ng=1 I2 (vdd Vref Vref vdd) modp w=10u l=2u as=2.3e-11 ad=2.3e-11 ps=14.6u \ pd=14.6u nrd=0.13 nrs=0.13 ng=1 ends Basic_Multiplier_Biasing // End of subcircuit definition. // Library name: pd3 // Cell name: LinearRegion_MOS_Multiplier1_CoupledLoad Page 102 // View name: schematic subckt LinearRegion_MOS_Multiplier1_CoupledLoad Vout\+ Vout\- Vref Vx1\+ \ Vx1\- Vx2\+ Vx2\- Vy1\+ Vy1\- Vy2\+ Vy2\- vdd vss vtie I41 (V\+ V\- vdd vdd) modp w=35u l=2u as=8.05e-11 ad=8.05e-11 ps=39.6u pd=39.6u nrd=0.0371429 nrs=0.0371429 ng=1 I39 (V\- V\+ vdd vdd) modp w=35u l=2u as=8.05e-11 ad=8.05e-11 ps=39.6u pd=39.6u nrd=0.0371429 nrs=0.0371429 ng=1 I44 (net054 Vref vdd vdd) modp w=50u l=2u as=1.15e-10 ad=1.15e-10 \ ps=54.6u pd=54.6u nrd=0.026 nrs=0.026 ng=1 I10 (V\+ V\+ vdd vdd) modp w=50u l=2u as=1.15e-10 ad=1.15e-10 ps=54.6u pd=54.6u nrd=0.026 nrs=0.026 ng=1 I11 (V\- V\- vdd vdd) modp w=50u l=2u as=1.15e-10 ad=1.15e-10 ps=54.6u pd=54.6u nrd=0.026 nrs=0.026 ng=1 I30 (V\+ Vy2\- net0117 vtie) npn111 area=2 m=1 I31 (V\- Vy2\- net0113 vtie) npn111 area=2 m=1 I32 (V\- Vy2\+ net0109 vtie) npn111 area=2 m=1 I33 (V\+ Vy2\+ net0105 vtie) npn111 area=2 m=1 I19 (vdd net054 net060 vtie) npn111 area=2 m=1 I16 (net054 net060 vss vtie) npn111 area=2 m=1 I14 (net058 net060 vss vtie) npn111 area=2 m=1 I5 (V\+ Vy1\- net26 vtie) npn111 area=2 m=1 I4 (V\- Vy1\- net30 vtie) npn111 area=2 m=1 I2 (V\- Vy1\+ net34 vtie) npn111 area=2 m=1 I1 (V\+ Vy1\+ net38 vtie) npn111 area=2 m=1 I43 (vdd vdd Vout\- vtie) modn w=5u l=2u as=1.15e-11 ad=1.15e-11 \ ps=9.6u pd=9.6u nrd=0.26 nrs=0.26 ng=1 I34 (net0117 Vx2\- vss vtie) modn w=4.5u l=2u as=1.035e-11 \ ad=1.035e-11 ps=9.1u pd=9.1u nrd=0.288889 nrs=0.288889 ng=1 I35 (net0113 Vx2\+ vss vtie) modn w=4.5u l=2u as=1.035e-11 \ ad=1.035e-11 ps=9.1u pd=9.1u nrd=0.288889 nrs=0.288889 ng=1 I36 (net0109 Vx2\- vss vtie) modn w=4.5u l=2u as=1.035e-11 \ ad=1.035e-11 ps=9.1u pd=9.1u nrd=0.288889 nrs=0.288889 ng=1 I37 (net0105 Vx2\+ vss vtie) modn w=4.5u l=2u as=1.035e-11 \ ad=1.035e-11 ps=9.1u pd=9.1u nrd=0.288889 nrs=0.288889 ng=1 I42 (vdd vdd Vout\+ vtie) modn w=5u l=2u as=1.15e-11 ad=1.15e-11 \ ps=9.6u pd=9.6u nrd=0.26 nrs=0.26 ng=1 I20 (Vout\- V\+ net058 vtie) modn w=15u l=2u as=3.45e-11 ad=3.45e-11 \ ps=19.6u pd=19.6u nrd=0.0866667 nrs=0.0866667 ng=1 I21 (Vout\+ V\- net058 vtie) modn w=15u l=2u as=3.45e-11 ad=3.45e-11 \ ps=19.6u pd=19.6u nrd=0.0866667 nrs=0.0866667 ng=1 I7 (net26 Vx1\- vss vtie) modn w=4.5u l=2u as=1.035e-11 ad=1.035e-11 \ ps=9.1u pd=9.1u nrd=0.288889 nrs=0.288889 ng=1 I6 (net30 Vx1\+ vss vtie) modn w=4.5u l=2u as=1.035e-11 ad=1.035e-11 \ ps=9.1u pd=9.1u nrd=0.288889 nrs=0.288889 ng=1 I3 (net34 Vx1\- vss vtie) modn w=4.5u l=2u as=1.035e-11 ad=1.035e-11 \ ps=9.1u pd=9.1u nrd=0.288889 nrs=0.288889 ng=1 I0 (net38 Vx1\+ vss vtie) modn w=4.5u l=2u as=1.035e-11 ad=1.035e-11 \ ps=9.1u pd=9.1u nrd=0.288889 nrs=0.288889 ng=1 ends LinearRegion_MOS_Multiplier1_CoupledLoad // End of subcircuit definition. // Library name: pd3 // Cell name: MOS_LInearRegion_Multiplier_singletodiff1 // View name: schematic subckt MOS_LInearRegion_Multiplier_singletodiff1 I\+ I\- Vref diff1\+ \ diff1\- diff2\+ diff2\- vdd vss vtie I29 (diff1\- Vref vdd vdd) modp w=20u l=2u as=4.6e-11 ad=4.6e-11 \ \ \ \ \ Page 103 ps=24.6u pd=24.6u nrd=0.065 nrs=0.065 ng=1 I23 (vss diff2\- diff1\- diff1\-) modp w=25u l=2u as=5.75e-11 \ ad=5.75e-11 ps=29.6u pd=29.6u nrd=0.052 nrs=0.052 ng=1 I24 (vss diff2\+ diff1\+ diff1\+) modp w=25u l=2u as=5.75e-11 \ ad=5.75e-11 ps=29.6u pd=29.6u nrd=0.052 nrs=0.052 ng=1 I28 (diff1\+ Vref vdd vdd) modp w=20u l=2u as=4.6e-11 ad=4.6e-11 \ ps=24.6u pd=24.6u nrd=0.065 nrs=0.065 ng=1 I38 (net63 Vref vdd vdd) modp w=50u l=2u as=1.15e-10 ad=1.15e-10 \ ps=54.6u pd=54.6u nrd=0.026 nrs=0.026 ng=1 I12 (vdd vdd diff2\- vtie) modn w=2.5u l=2u as=5.75e-12 ad=5.75e-12 \ ps=7.1u pd=7.1u nrd=0.52 nrs=0.52 ng=1 I9 (diff2\- I\+ net24 vtie) modn w=3.5u l=2u as=8.05e-12 ad=8.05e-12 \ ps=8.1u pd=8.1u nrd=0.371429 nrs=0.371429 ng=1 I11 (vdd vdd diff2\+ vtie) modn w=2.5u l=2u as=5.75e-12 ad=5.75e-12 \ ps=7.1u pd=7.1u nrd=0.52 nrs=0.52 ng=1 I10 (diff2\+ I\- net24 vtie) modn w=3.5u l=2u as=8.05e-12 ad=8.05e-12 \ ps=8.1u pd=8.1u nrd=0.371429 nrs=0.371429 ng=1 I71 (net24 net59 vss vtie) npn111 area=2 m=1 I73 (vdd net63 net59 vtie) npn111 area=2 m=1 I72 (net63 net59 vss vtie) npn111 area=2 m=1 ends MOS_LInearRegion_Multiplier_singletodiff1 // End of subcircuit definition. // Library name: pd3 // Cell name: LinearRegion_MOS_Multiplier_2ndStage // View name: schematic subckt LinearRegion_MOS_Multiplier_2ndStage I\+ I\- Vx\+ Vx\- Vy\+ Vy\- \ vdd vss vtie I47 (I\+ net0144 vdd vdd) modp w=100u l=2u as=2.3e-10 ad=2.3e-10 \ ps=104.6u pd=104.6u nrd=0.013 nrs=0.013 ng=1 I46 (I\- net0109 vdd vdd) modp w=100u l=2u as=2.3e-10 ad=2.3e-10 \ ps=104.6u pd=104.6u nrd=0.013 nrs=0.013 ng=1 I10 (net0144 net0144 vdd vdd) modp w=50u l=2u as=1.15e-10 ad=1.15e-10 \ ps=54.6u pd=54.6u nrd=0.026 nrs=0.026 ng=1 I11 (net0109 net0109 vdd vdd) modp w=50u l=2u as=1.15e-10 ad=1.15e-10 \ ps=54.6u pd=54.6u nrd=0.026 nrs=0.026 ng=1 I5 (net0144 Vy\- net26 vtie) npn111 area=2 m=1 I4 (net0109 Vy\- net30 vtie) npn111 area=2 m=1 I2 (net0109 Vy\+ net34 vtie) npn111 area=2 m=1 I1 (net0144 Vy\+ net38 vtie) npn111 area=2 m=1 I7 (net26 Vx\- vss vtie) modn w=15u l=2u as=3.45e-11 ad=3.45e-11 \ ps=19.6u pd=19.6u nrd=0.0866667 nrs=0.0866667 ng=1 I6 (net30 Vx\+ vss vtie) modn w=15u l=2u as=3.45e-11 ad=3.45e-11 \ ps=19.6u pd=19.6u nrd=0.0866667 nrs=0.0866667 ng=1 I3 (net34 Vx\- vss vtie) modn w=15u l=2u as=3.45e-11 ad=3.45e-11 \ ps=19.6u pd=19.6u nrd=0.0866667 nrs=0.0866667 ng=1 I0 (net38 Vx\+ vss vtie) modn w=15u l=2u as=3.45e-11 ad=3.45e-11 \ ps=19.6u pd=19.6u nrd=0.0866667 nrs=0.0866667 ng=1 ends LinearRegion_MOS_Multiplier_2ndStage // End of subcircuit definition. // Library name: pd3 // Cell name: pd_L2 // View name: schematic subckt pd_L2 I\+ I\- I_Iout\+ I_Iout\- Q\+ Q\- Q_Iout\+ Q_Iout\- c3i1\+ \ c3i1\- c3i2\+ c3i2\- c3q1\+ c3q1\- c3q2\+ c3q2\- vbg_out1 vbg_out2 \ vdd_I vdd_Q vdd_bg vss_I vss_Q vss_bg vtie Page 104 I94 (vss_bg ibg_1mI ibg_1mQ vss_bg vss_bg vss_bg vss_bg Iref_0 Iref_1 \ vbg_out1 vbg_out1 vbg_out2 vdd_bg vss_bg vtie) bandgap C8 (vdd_bg vss_bg vtie) cpolybr3 area=1.12515e-08 perimeter=424.292u \ np=1 csub=876.071f rsub=9.42369 rp1=16.6766 rp2=68.454 C7 (vdd_bg vss_bg vtie) cpolybr3 area=8.46143e-08 \ perimeter=1163.54000u np=1 csub=6.05177p rsub=5.26147 rp1=43.0283 \ rp2=74.2122 C1 (vdd_I vss_I vtie) cpolybr3 area=1.68757e-08 perimeter=649.663u \ np=1 csub=1.31554p rsub=13.8984 rp1=23.6394 rp2=25.6605 C2 (vdd_Q vss_Q vtie) cpolybr3 area=1.68757e-08 perimeter=649.663u \ np=1 csub=1.31554p rsub=13.8984 rp1=23.6394 rp2=25.6605 C10 (vdd_Q vss_Q vtie) cpolybr3 area=1.68841e-08 perimeter=575.323u \ np=1 csub=1.2973p rsub=11.0594 rp1=21.2079 rp2=33.3666 C6 (vdd_bg vss_bg vtie) cpolybr3 area=8.46143e-08 \ perimeter=1163.54000u np=1 csub=6.05177p rsub=5.26147 rp1=43.0283 \ rp2=74.2122 C3 (vdd_Q vss_Q vtie) cpolybr3 area=1.12505e-08 perimeter=433.018u \ np=1 csub=878.212f rsub=10.3053 rp1=16.527 rp2=47.9771 C9 (vdd_I vss_I vtie) cpolybr3 area=1.68841e-08 perimeter=575.323u \ np=1 csub=1.2973p rsub=11.0594 rp1=21.2079 rp2=33.3666 C0 (vdd_I vss_I vtie) cpolybr3 area=1.12505e-08 perimeter=433.018u \ np=1 csub=878.212f rsub=10.3053 rp1=16.527 rp2=47.9771 C5 (vdd_I vss_I vtie) cpolybr3 area=1.12505e-08 perimeter=433.018u \ np=1 csub=878.212f rsub=10.3053 rp1=16.527 rp2=47.9771 I26 (net0155 net0154 I_Iout\+ I_Iout\- Vref vdd_I vss_I vtie ibg_1mI) \ pd_output_top I27 (net087 net0162 Q_Iout\+ Q_Iout\- Vref vdd_Q vss_Q vtie ibg_1mQ) \ pd_output_top I9 (net69 net0103 Vref I_1\+ I_1\- Q_1\+ Q_1\- net085 net0115 net0106 \ net0113 vdd_Q vss_Q vtie) LinearRegion_MOS_Multiplier2_CoupledLoad I8 (net0117 net0116 Vref I_1\+ I_1\- Q_1\+ Q_1\- net0173 net0172 \ net0164 net0163 vdd_I vss_I vtie) \ LinearRegion_MOS_Multiplier2_CoupledLoad I3 (net0155 net0154 I\+ I\- Vref vdd_I vss_I vtie) \ transconductor1_test I4 (net087 net0162 Q\+ Q\- Vref vdd_Q vss_Q vtie) transconductor1_test I14 (Iref_0 Vref vdd_bg vss_bg vtie) Basic_Multiplier_Biasing I5 (net76 net75 Vref I_1\+ I_1\- Q_1\+ Q_1\- net64 net0151 net0150 \ net0157 vdd_I vss_I vtie) LinearRegion_MOS_Multiplier1_CoupledLoad I22 (c3i1\+ c3i1\- Vref net0175 net0174 net0173 net0172 vdd_I vss_I \ vtie) MOS_LInearRegion_Multiplier_singletodiff1 I23 (c3q1\+ c3q1\- Vref net0166 net0165 net0164 net0163 vdd_I vss_I \ vtie) MOS_LInearRegion_Multiplier_singletodiff1 I7 (c3i2\+ c3i2\- Vref net082 net44 net0106 net0113 vdd_Q vss_Q vtie) \ MOS_LInearRegion_Multiplier_singletodiff1 I6 (c3q2\+ c3q2\- Vref net52 net084 net085 net0115 vdd_Q vss_Q vtie) \ MOS_LInearRegion_Multiplier_singletodiff1 I13 (Q\+ Q\- Vref Q_1\+ Q_1\- net0150 net0157 vdd_Q vss_Q vtie) \ MOS_LInearRegion_Multiplier_singletodiff1 I12 (I\+ I\- Vref I_1\+ I_1\- net64 net0151 vdd_I vss_I vtie) \ MOS_LInearRegion_Multiplier_singletodiff1 I2 (net087 net0162 net76 net75 net69 net0103 vdd_Q vss_Q vtie) \ LinearRegion_MOS_Multiplier_2ndStage I15 (net0155 net0154 net76 net75 net0117 net0116 vdd_I vss_I vtie) \ LinearRegion_MOS_Multiplier_2ndStage ends pd_L2 // End of subcircuit definition. Page 105 // Library name: cartesian // Cell name: PPA2C_try // View name: schematic subckt PPA2C_try PVSSR3 VDDA vtie I4 (vtie PVSSR3) nd area=1.5344e-09 perimeter=0.00157303 m=1 I3 (vtie VDDA) nd area=1.3364e-09 perimeter=0.00118103 m=1 I5 (vtie PVSSR3) nwd area=2.2656e-09 perimeter=0.0007792 m=1 I7 (vtie VDDA) nwd area=1.32744e-08 perimeter=0.0008036 m=1 ends PPA2C_try // End of subcircuit definition. // Library name: cartesian // Cell name: shield_cold_try // View name: schematic subckt shield_cold_try P SHIELD VCC VEE R1 (net16 SHIELD) resistor r=19 I7 (VEE net16) nwd area=8.827n perimeter=319.169u m=1 C17 (net16 VEE) capacitor c=30f m=1 C9 (net16 VCC) capacitor c=25f m=1 C7 (net16 P) capacitor c=165f m=1 ends shield_cold_try // End of subcircuit definition. // Library name: cartesian // Cell name: esd_redu_try // View name: schematic subckt esd_redu_try A P VCC VEE vtie R0 (A VCC P) rdiffp3 w=10u l=12.2u m=1 I8 (vtie VCC) nwd area=4.384n perimeter=845.2u m=1 I10 (vtie P) nwd area=340.8p perimeter=137.6u m=1 I15 (vtie VEE) nwd area=1.194n perimeter=410u m=1 I9 (vtie VCC) nd area=1.086n perimeter=1206.000u m=1 I14 (vtie VEE) nd area=1.43664e-09 perimeter=1035.15000u m=1 I13 (vtie P) nd area=891p perimeter=478u m=1 I11 (P VCC) pd area=661p perimeter=195u m=1 I12 (A VCC) pd area=168p perimeter=54u m=1 C3 (VCC P) capacitor c=62.92f m=1 C15 (A vtie) capacitor c=6.28f m=1 C13 (VCC vtie) capacitor c=228.88f m=1 C5 (VCC A) capacitor c=23.53f m=1 C11 (vtie P) capacitor c=48.24f m=1 ends esd_redu_try // End of subcircuit definition. // Library name: cartesian // Cell name: rfcold_try // View name: schematic subckt rfcold_try A1 A2 P1 P2 SHIELD VCC VEE vtie I1 (P1 SHIELD VCC vtie) shield_cold_try I2 (P2 SHIELD VCC vtie) shield_cold_try I0 (A1 P1 VCC VEE vtie) esd_redu_try I3 (A2 P2 VCC VEE vtie) esd_redu_try ends rfcold_try // End of subcircuit definition. // Library name: cartesian Page 106 // Cell name: IOA2C_try // View name: schematic subckt IOA2C_try A IO VDD VSS vtie I23 (vtie IO) nd area=2.66696e-09 perimeter=0.00135448 m=1 I26 (vtie VDD) nd area=1.3892e-09 perimeter=0.00178851 m=1 I28 (vtie VSS) nd area=1.80339e-09 perimeter=0.000992085 m=1 I24 (vtie IO) nwd area=8.4495e-09 perimeter=0.000705 m=1 I25 (vtie VDD) nwd area=7.38318e-09 perimeter=0.0011918 m=1 I27 (vtie VSS) nwd area=8.04e-10 perimeter=0.00028 m=1 I22 (IO VDD) pd area=8.9824e-10 perimeter=0.000289685 m=1 I21 (A VDD) pd area=3.7e-11 perimeter=2.74e-05 m=1 R0 (A VDD IO) rdiffp3 w=10u l=8e-05 m=1 ends IOA2C_try // End of subcircuit definition. // Library name: cartesian // Cell name: PPA1C_try // View name: schematic subckt PPA1C_try VSSA ends PPA1C_try // End of subcircuit definition. // Library name: pd3 // Cell name: pd_ring // View name: schematic subckt pd_ring I\+ I\- Q\+ Q\- VoutI\+ VoutI\- VoutQ\+ VoutQ\- _I\+ _I\- \ _Q\+ _Q\- _VoutI\+ _VoutI\- _VoutQ\+ _VoutQ\- _c3i1\+ _c3i1\- \ _c3i2\+ _c3i2\- _c3q1\+ _c3q1\- _c3q2\+ _c3q2\- _vbg_out1 \ _vbg_out2 c3i1\+ c3i1\- c3i2\+ c3i2\- c3q1\+ c3q1\- c3q2\+ c3q2\- \ vbg_out1 vbg_out2 vdd_I vdd_Q vdd_bg vss_I vss_Q vss_bg vtie I27 (vss_Q vdd_Q vtie) PPA2C_try I34 (vss_bg vdd_bg vtie) PPA2C_try I2 (vss_I vdd_I vtie) PPA2C_try I22 (VoutQ\+ VoutQ\- _VoutQ\+ _VoutQ\- vss_Q vdd_Q vss_Q vtie) \ rfcold_try I0 (VoutI\+ VoutI\- _VoutI\+ _VoutI\- vss_I vdd_I vss_I vtie) \ rfcold_try I23 (c3i2\+ _c3i2\+ vdd_Q vss_Q vtie) IOA2C_try I24 (c3i2\- _c3i2\- vdd_Q vss_Q vtie) IOA2C_try I25 (c3q2\+ _c3q2\+ vdd_Q vss_Q vtie) IOA2C_try I26 (c3q2\- _c3q2\- vdd_Q vss_Q vtie) IOA2C_try I35 (vbg_out2 _vbg_out2 vdd_bg vss_bg vtie) IOA2C_try I29 (vbg_out1 _vbg_out1 vdd_bg vss_bg vtie) IOA2C_try I9 (I\- _I\- vdd_I vss_I vtie) IOA2C_try I3 (c3q1\+ _c3q1\+ vdd_I vss_I vtie) IOA2C_try I4 (c3q1\- _c3q1\- vdd_I vss_I vtie) IOA2C_try I5 (c3i1\+ _c3i1\+ vdd_I vss_I vtie) IOA2C_try I6 (c3i1\- _c3i1\- vdd_I vss_I vtie) IOA2C_try I8 (I\+ _I\+ vdd_I vss_I vtie) IOA2C_try I11 (Q\+ _Q\+ vdd_Q vss_Q vtie) IOA2C_try I12 (Q\- _Q\- vdd_Q vss_Q vtie) IOA2C_try I28 (vss_Q) PPA1C_try I30 (vtie) PPA1C_try I36 (vss_bg) PPA1C_try I1 (vss_I) PPA1C_try I7 (vss_I) PPA1C_try Page 107 I14 (vss_Q) PPA1C_try I44 (vss_I) PPA1C_try ends pd_ring // End of subcircuit definition. // // // I1 Library name: pd3 Cell name: pd_top1 View name: schematic (net36 net35 net18 net024 net016 net017 net023 net15 net015 net014 \ net24 net23 net011 net21 net20 net19 net2 net1 net066 net065 \ net064 net0124 net0123 net061 net060) pd_L2 I0 (net36 net35 net016 net017 net18 net024 net023 net15 net098 net097 \ net096 net095 net0116 net0115 net0114 net0113 net094 net093 net092 \ net091 net090 net089 net088 net087 net0112 net0111 net015 net014 \ net24 net23 net011 net21 net20 net19 net2 net1 net066 net065 \ net064 net0124 net0123 net061 net060) pd_ring simulatorOptions options reltol=100e-6 vabstol=1e-6 iabstol=1e-12 temp=27 \ tnom=27 homotopy=all limit=delta scalem=1.0 scale=1.0 \ compatible=spice2 gmin=1e-12 rforce=1 maxnotes=5 maxwarns=5 digits=5 \ cols=80 pivrel=1e-3 ckptclock=1800 sensfile="../psf/sens.output" saveOptions options save=allpub Page 103 [...]... switches Page 8 DC RFC Filtering/ Matching Network Vin Figure 2.1 RL Basic Circuit Diagram for Power Amplifier Figure 2.1 shows the basic circuit diagram for all the power amplifiers [1] The radio frequency choke (RFC) feeds the DC power to the drain of the BJT It is to provide low impedance for the bias but high impedance for a.c signals The BJT could also be replaced by other types of transistor... systems, it will open up a whole range of services to the consumers One of the major enabling device for 3G or future cellular systems is the transceiver Page 2 It consists of the two major blocks, the receiver and transmitter The receiver receives information from air Whereas the transmitter transmits information generated by the cellular terminals to the air It is thus front end of cellular communication... the current will conduct at all times But the conduction angle is 180 degrees and below 180 degrees Page 9 for class B and C power amplifiers respectively The linearity for class A power amplifiers is the best followed by B and C But the power efficiency is the lowest for class A and highest for class C A compromise between linearity and power efficiency is met by class AB power amplifiers Class E... system (i.e OFDM) 2.4.1 Two Tones Test The two-tone test is the standard test for linearity of the power amplifier Figure 2.6 shows how the two-tone test is performed It is to input two frequency tones to the power amplifier For a narrow band system, the frequency spacing of the two tones is estimated to be the bandwidth of the transmitter At the output of the power amplifier, other frequency components,... the overall system Also the couplers and splitters used are passive, therefore lossy, components This will also decrease the efficiency of the overall system Feedforward linearization is an open loop linearization Therefore it has much greater bandwidth compared to feedback linearization It is possible to obtain good linearity performance It is normally used in base stations Page 21 2.5.3 Envelope Elimination...Chapter 1 Introduction 1.1 Background The primary purpose of any wireless communication systems is to transmit or receive information The information could be in any form such as speech, pictures or data In the area of cellular and personal communication service (PCS) systems, there is a trend of transmitting data and video instead of merely speech... Power Amplifier One of the major blocks of the transmitter is the power amplifier [2] This component consumes the most power of the transceiver [3] For example, RF MicroDevices’s RF2161 [4] or Raytheon’s RTPA5250-130 [5] consume 0.4W and 0.66W respectively To achieve higher data rate and be spectrally efficient, communication systems use linear modulation for example QAM (Quadrature Amplitude Modulation)... transmitted Therefore even order frequency components do not fall into the bandwidth of the transmitter and could be filtered out Using the power series, it is able to model the 1db compression point, gain and phase distortion But the distortion caused by the higher order in the power series is very low The most serious distortion is caused by third and maybe the fifth order in the power series Therefore most... will affect the power consumption of the transmitter Being the most power consuming block of the transceiver, any reduction in power consumption will reduce the power consumption of the whole transceiver system A reduction of power consumption will increase the talk time of the communication equipment This is especially important for cellular mobile phones Therefore there is a compromise between the... also acquaints himself the general techniques that are used to improve the linearity of the power amplifier namely feedback, feedforward and predistortion The next chapter, chapter 3, the design of the new analog predistorter is described This shall include the architecture and circuit In chapter 4, the chip was used to linearise an actual RF power amplifier The chip was tested at IF and baseband Two-tone .. .Circuit Design for Linearizing Transmitter Sim Chan Kuen, (B Eng., Nanyang Technological University) DEPARTMENT OF ELECTRICAL ENGINEERING A THESIS SUBMITTED FOR THE DEGREE OF... tones for ROF predistortion two-tones test (after linearization) 82 4.25 Two-tones test for ROF system 83 4.26 Multi-Carrier Test for ROF system(Before Linearization) 85 4.27 Multi-Carrier Test for. .. two-tones test (before linearization) 4.22 Zooming on the frequency spectrum around the two tones for ROF predistortion two-tones test (before linearization) 4.23 81 Overall output spectrum for ROF predistortion