SIMSIDES User Guide
Contents
1. SC F hh Integrator All Effects SC LD Integrator All Effects switch on resistance capacitor nonlinearity and mismatch settling error finite nonlinear DC gain thermal noise parasitic load capacitors output swing limitation SC FE Integrator All Effects amp NonLinSamp SC LD Integrator All Effects amp NonLinSamp switch nonlinear on resistance capacitor nonlinearity and mismatch settling error finite nonlinear DC gain thermal noise parasitic load capacitors output swing limitation SC F E Int 1b SD2 switch on resistance and its effect on GB and SR capacitor nonlinearity and mismatch settling error finite nonlinear DC gain thermal noise parasitic load capacitors output swing limitation SC F hh Tut 1b DEM SD2 switch on resistance and its effect on GB and SR array of unit sampling capacitors capacitor nonlinearity and mismatch settling error finite nonlinear DC gain thermal noise parasitic load capacitors output swing limitation 26 SIMSIDES Block Libraries and Models Table 2 3 Parameter name in alphabetical order Model parameters used in SIMSIDES SC FE LD integrators Brief description Array of sampling capacitors for DEM branch Array of unit capacitors used with multilevel DACs with DEM B switch parameters MOS large signal transconductance analytic model Bandwidth BW Input si2. Seed for random jitter generation Seed number used for generating random jitter error 34 SIMSIDES Block Libraries and Models SIMSIDES CT Building Block Libraries Integrators Resonators MOSFET C Active RC Figure 2 2 Classification of SIMSIDES CT model libraries 2 5 Real D A Converters Table 2 13 lists the different building blocks included in the real D A Converters SIM SIDES library together with a brief description of their operation and main circuit errors Error parameters associated to the models listed in Table 2 13 have the same meaning as those used in multibit quantizers except for the selectable NRZ RZ HRZ DAC waveform and the delay error The latter can be chosen to be either a constant delay or a signal dependent delay given by delay v d0 lt dmax 2 1 dl x1 v where d0 d1 x1 dmax are model parameters set by the user 2 6 Auxiliary Blocks In addition to the building blocks described in previous sections SIMSIDES includes a library named Auxiliary blocks that contains some other blocks like adders DEM algorithms and digital latches also needed to simulate SAMs Table 2 14 lists the models included in the mentioned library together with a brief description of their operation The most significant parameters used by these models are listed in Table 2 15 SIMSIDES Block Libraries and Models 35 Table 2 13 Model name Real DAC models included in SIMSIDES
3. Digital output code 1 Binary output 2 Trilevel output including common mode Default 1 Time interval between sampling and comparison delta Delay between the time instant when the adding operation is performed and the time instant when comparison time takes place
4. Temperature K Transconductance of the AO gm OTA transconductance Variance Variance of the capacitor mismatch error SIMSIDES Block Libraries and Models 27 l i l Csi Basic SC FE Int oo ps eus Ed A 2 o v oo 1 7 E Xe oy o N s A T Yo Vou a b Figure 2 1 SC integrator symbol in SIMSIDES a One branch integrator b Two branch integrator 2 3 Real CT Building Block Libraries Figure 2 2 shows the CT building block model libraries included in SIMSIDES There are four libraries of CT integrators and two libraries of CT resonators which are classified attending to the circuit nature of the building blocks namely Gm C Gm MC Gm LC active RC and MOSFET C 2 3 1 Real CT Integrators Tables 2 5 2 8 list all models included in CT integrator libraries shown in Figure 2 2 together with a brief description of the nonideal effects included 2 3 2 Real CT Resonators Tables 2 9 and 2 10 list all models included in CT resonator libraries shown in Figure 2 2 together with a brief description of their nonideal effects These libraries include different building blocks that are classified according to the accuracy of their models as well as to the circuit nonidealities that are taken into account RC_Int_1 2 3in models allow to set up transistor level parameters such as channel length modulation gate to source overdrive voltage saturation voltage supply voltage
5. Circuit effects included Real_DAC_Multibit Voltage mode multibit DAC with offset gain error and INL error Real_DAC_Multibit_SI Current mode multibit DAC with offset gain error and INL error Real_DAC_Multibit_delay_Jitter Voltage mode multibit DAC with offset error gain error INL error delay error and clock jitter error Real_DAC_Multibit_delay_Jitter_SI Current mode multibit DAC with finite output conductance offset error gain error INL error delay error and clock jitter error Real_DAC_pulse_types Voltage mode multibit DAC with selectable NRZ RZ HRZ output waveform Real_DAC_Multibit_pulse_types Voltage mode multibit DAC with selectable NRZ RZ HRZ output waveform gain error offset error and INL error Real_DAC _delay_jitter Voltage mode multibit DAC with selectable NRZ RZ HRZ output waveform gain error offset error INL error delay error and clock jitter error 36 SIMSIDES Block Libraries and Models Table 2 14 Auxiliary building block models used in SIMSIDES ANALOG ADDERS Model name Brief description Analog_Adder_Ideal_SD2 Ideal SC passive adder with parasitic input capacitance and load capacitance Analog_Adder_real_SD2 Real SC passive adder with parasitic input capacitance and load capacitance switch on resistance settling error capacitor nonlinearity and thermal noise Model name DIGITAL ADDERS Bri
6. computing the harmonic distortion power Two different figures of merit can be calculated namely THD and third order intermodulation distortion 1M3 in Figure 1 8 The latter requires using a two tone input signal For that reason there is an additional parameter named Input2 Frequency that defines the frequency of the second input tone Integral and Differential Non Linearity The INTEGRAL AND DIFFERENTIAL NON LINEARITY menu illustrated in Figure 1 9 is used for characterizing the static linearity in SIMSIDES The analysis is based on either Histograms or Input Ramp Waveform selected by the user Other parameters required to do this analysis are the Input Amplitude and the Number of bits which specifies the ideal resolution of the A D conversion expressed in bits File Edit Analysis Optimization Help Figure 1 7 SNR SNDR menu SIMSIDES User Guide 9 File Edit Analysis Optimization Help Figure 1 8 Harmonic distortion analysis menu File Edit Analysis Optimization Help 3 Ein Y Hystograms M Figure 1 9 Integral and differential non linearity analysis menu 10 SIMSIDES User Guide Multi Tone Power Ratio SIMSIDES can also analyze the harmonic distortion in those telecom applications such as ADSL where a discrete multi tone DMT signal is used In this case the linearity of the system is measured by a figure named multi tone power ratio MTPR The corresponding SIMSIDES menu sh
7. pole dynamic thermal noise SIMSIDES Block Libraries and Models 33 Table 2 11 Real Quantizers and Comparator models included in SIMSIDES Model name Circuit effects included Real Comparator Offset amp Hysteresis Voltage mode comparator with offset random amp deterministic hysteresis Real Comparator Offset amp Hysteresis for SI Current mode comparator with offset and nonlinearity INL Real Multibit Quantizer Voltage mode multibit quantizer with gain error offset random amp deterministic hysteresis Real Multibit Quantizer for SI Current mode multibit quantizer with gain error offset INL random amp deterministic hysteresis Real Multibit Quantizer dig level SD2 Voltage mode multilevel quantizer with gain error offset INL random amp deterministic hysteresis Real Sampler Sampling amp Hold circuit with clock jitter error Table 2 12 Error model parameters used in SIMSIDES Real Quantizers Parameter name in alphabetical order Brief description Gain Error in LSB Gain error measured in LSB Jitter typical deviation Standard deviation of clock jitter error Kind of Hysteresis Comparator hysteresis It may be either deterministic or random hysteresis INL in LSB Integral Nonlinearity error measured in LSB Number of levels Number of quantizer levels Offset Offset error Offset Error in LSB Offset error measured in LSB
8. C circuits Note that although single ended conceptual schematics are shown in this figure fully differential circuits are assumed in the behavioral models Both integrators in Figure 2 1 use the same behavioral model which consists of an ideal SC FE integrator with output swing limitation The behavioral model corresponding to a one branch SC FE integrator is named Basic SC FE Int while the model of the two branch SC FE integrator is named Basic SC FE IntII Following this nomenclature Basic SC FE IntIII and Basic SC FE IntIV models are used for three and four branch SC FE integrators respectively Extracted from the book CMOS Sigma Delta Converters Practical Design Guide Jos M de la Rosa and Roc o del R o c 2013 John Wiley amp Sons Ltd Published 2013 by John Wiley amp Sons Ltd 24 SIMSIDES Block Libraries and Models Table 2 1 Overview of SIMSIDES libraries Ideal Libraries Sublibraries Building Blocks Integrators Ideal DT CT integrators Resonators Ideal resonators Quantizers amp Comparators Ideal quantizers D A Converters Ideal DACs Real Libraries Sublibraries Building Blocks Integrators SC FE integrators Forward Euler SC integrators SC LD integrators Lossless Direct SC integrators SI FE integrators Forward Euler SI integrators SI LD integrators Lossless Direct SI integrators gm C integrators Gm C integrators gm MC integrators Miller OTA integrators RC integrators Active R
9. C integrators MOSFET C integrators MOSFET C integrators Resonators SC FE resonators Resonators based on FE SC integrators SC LD resonators SI FE resonators SI LD resonators gm C resonators gm LC resonators Resonators based on LD SC integratorss Resonators based on FE SI integrators Resonators based on LD SI integrators Resonators based on Gm C integrators Resonators based on Gm LC integrators Quantizers amp Comparators Nonideal single bit amp multibit quantizers D A Converters Nonideal single bit and multibit DACs Auxiliary Blocks Adders latches DEM blocks etc Table 2 2 lists all SC integrator models available in SIMSIDES including a brief description of the nonidealities included in each of them Note that the model names included in Table 2 2 correspond to one branch integrators The same models are available for integrators with up to four input branches Table 2 3 lists the most important parameters used by the SC integrator behavioral models in SIMSIDES as well as a brief description of all of them 2 2 2 Real SC Resonators SIMSIDES has two SC resonator model libraries corresponding to FEI based resonators and LDI based resonators Following the same philosophy as that used in SC integrators the behavioral models of SC resonators in SIMSIDES are classified attending to the number of input SC branches and the circuit nonideal effects included in the models Table 2 4 lists all SC resonator models ava
10. IMULINK ie choosing Simulation Start menu in the SIMULINK model window 13 Analyzing SAMs in SIMSIDES Simulation output data can be post processed in SIMULINK using the Analysis menu As illustrated in Figure 1 4 the Analysis menu includes the following submenus e Node Spectrum Analysis which computes and plots the FFT magnitude spectrum of a given signal e Integrated Power Noise used for calculating and graphically representing the IBN within a given signal bandwidth SIMSIDES User Guide 3 55 2 2 E H All changes take effect immediately Add Folder Add with Subfolders Move to Top Move Up Move Down Move to Bottom MATLAB search path L3 Users josemdelarosa HOME MATLAB SIMSIDES__2_0 E Users josemdelarosa HOME MATLAB SIMSIDES 2 O Compilations L3 Users josemdelarosa HOME MATLAB SIMSIDES 2 O Compilations Linux E Users josemdelarosa HOME MATLAB SIMSIDES 2 O0 Compilations Linux E Users josemdelarosa HOME MATLAB SIMSIDES 2 O Compilations Linux E Users josemdelarosa HOME MATLAB SIMSIDES 2 O0 Compilations Linux E Users josemdelarosa HOME MATLAB SIMSIDES 2 O Compilations Linux C E Users josemdelarosa HOME MATLAB SIMSIDES 2 0 Compilations Linux C L3 Users josemdelarosa HOME MATLAB SIMSIDES 2 0 Compilations Linux t L3 Users josemdelarosa HOME MATLAB SIMSIDES 2 0 Compilations Linux
11. MSIDES by following the next steps Set up model parameters by using the M file shown in Figure 1 16 Simulate the modulator in Figure 1 15b from the menu Simulation gt Start Once the simulation has finished go to Analysis Node Spectrum Analysis menu in SIMSIDES Define the parameters requested in that menu In this example the sampling frequency is defined as s and a Kaiser window function is used with a number of points N and Beta 20 Click on Compute and then Plot and the output spectrum shown in Figure 1 17 is displayed Modulator Output Magnitude Spectrum 0 T T T Magnitude dB Qo eo 100 120r 140 60 i L L L L 10 10 10 10 Frequency Hz Figure 1 17 Output spectrum magnitude of the SAM in Figure 1 15b 18 SIMSIDES User Guide SNR versus Input Amplitude Level Figure 1 18 shows the SNDR versus input amplitude level or SNDR curve of the NAM in Figure 1 15b This figure has been obtained by using the Analysis menu and choosing SNR SNDR analysis In this example the following parameters are used e Parameter Name Ain where Ain is the Amplitude parameter defined in the Input Sine Wave block in Figure 1 15b e Range vi vf 1e 6 2 e N of points 50 e Scale Logarithmic e Analysis SNR SNDR e Second Parameter Off Once the aforementioned parameters are set up click on Continue and the SNR SNDR window menu shown in Figure 1 7 is displayed Th
12. SIMSIDES User Guide Jos M de la Rosa and Rocio del Rio Institute of Microelectronics of Seville IMSE CNM CSIC University of Seville E mail jrosa rocio imse cnm csic es Version 2 0 April 2013 CONTENTS 1 SIMSIDES User Guide 1 1 1 2 1 3 1 4 1 5 Getting Started Installing and Running SIMSIDES Building and Editing NAM Architectures in SIMSIDES Analyzing SAMs in SIMSIDES Example Getting Help 2 SIMSIDES Block Libraries and Models 2 1 22 2 3 2 4 2 6 Overview of SIMSIDES Libraries Real SC Building Block Libraries 2 2 1 Real SC Integrators 2 2 20 Real SC Resonators 2 2 3 Real CT Integrators Real CT Building Block Libraries 2 3 1 Real CT Resonators Real Quantizers amp Comparators Real D A Converters Auxiliary Blocks O9 b2 l2 j 23 23 23 23 24 27 27 27 28 34 34 1 SIMSIDES User Guide SIMSIDES SIMulink based SIgma DElta Simulator is a time domain behavioral simulator for NAMs that has been developed as a toolbox in the MATLAB SIMULINK environment SIMSIDES can be used for simulating any arbitrary XAM architecture implemented with both DT and CT circuit techniques To this end a complete list of SAM building blocks integrators resonators quantizers embedded DACs etc is included in the toolboox The behavioral models of these building blocks take into account the most critical error mechanisms of different circuit techniques including SC SI and CT circuits Thes
13. ameter to be varied This model parameter can be a variable used in a NAM building block model like for instance I Jm etc or a simulation parameter like the input signal amplitude sampling frequency etc e Range vi vf which defines the variation range defined by an interval with a lower value given by vi and a upper value of vf N of points i e the number of points in which the variation interval is divided e Scale that specifies if the variation range is either linear or logarithmic e Analysis that specifies the type of analysis to be carried out including output spectrum IBN SNR SNDR INL MTPR harmonic distortion histograms etc Monte Carlo Analysis Figure 1 13 shows the SIMSIDES menu to run a Monte Carlo analysis This is a particular case of parametric analysis which has essentially the same functionalities and model parameters The only difference is that the variation of the parameters involved in the Monte eoo SIMSIDES File Edit Analysis Optimization Help HISTOGRAM Name of the signal s to process it i2 i3 Number of bins Compute Cancel Figure 1 11 Histogram analysis menu 12 SIMSIDES User Guide File Edit Analysis Optimization Help ol He5 e3 100 pes1e4 10 Figure 1 12 Parametric analysis menu File Edit Analysis Optimization Help Figure 1 13 Monte Carlo analysis menu Carlo analysis are randomly varied according to a probability dist
14. an be output data generated in the simulations for instance the modulator output data stream which have been previously saved in the MATLAB workspace by using the To Workspace SIMULINK block Sampling frequency i e the sampling frequency in Hz Window which defines the window function used for computing the FFT The main window functions available in MATLAB can be selected namely Kaiser Barlett Blackman Hamming Hanning Chebyshev Boxcar and Triangular Number of Points i e the number of points N in Figure 1 5 for the selected window function and for FFT computation Window Parameters where other parameters required to define the window function are defined like Beta parameter used in Kaiser windows Once these parameters have been defined the output spectrum can be computed by clicking on the Compute button and then selecting the signal to be processed from the new window that is displayed Signal Spectrum window shown in Figure 1 5b Integrated Power Noise Figure 1 6 shows the SIMSIDES Integrated Power Node window used for computing the IBN of any arbitrary data sequence obtained from simulations To compute IBN the following parameters are required QOO SIMSIDES File Edit Analysis Optimization Help a b Figure 1 5 Node spectrum analysis menu SIMSIDES User Guide 7 File Edit Analysis Optimization Help Figure 1 6 Integrated power noise menu e Name of the signal s to proce
15. braries included in SIMSIDES together with a brief description of their contents These libraries are divided into two main categories ideal libraries and real libraries The former contains ideal building blocks whereas the latter includes behavioral models that incorporate circuit level nonidealities The libraries containing integrators and resonators are subdivided into several specific sublibraries which include in turn building block models corresponding to different circuit level implementations For instance SC integrators are subdivided into FE and LD integrators CT integrators are subdivided into Gm C active RC etc 2 2 Real SC Building Block Libraries SIMSIDES includes two libraries of SC integrators and two libraries of SC resonators These libraries are described below 2 2 1 Real SC Integrators There are two SC integrator model libraries in SIMSIDES one including FE SC integrator models and the other one including LD SC integrators In both cases integrator models are classified according to the nonideal effects that are included in the model and the number of SC branches connected at the integrator input This way for each model there are four building blocks using the same behavioral model except for the number of input SC branches As an illustration Figure 2 1 shows the symbol used in SIMSIDES for one branch SC FE integrators Figure 2 1a and two branch SC FE integrators Figure 2 1b together with their equivalent S
16. cting Edit gt SIMULINK Library or Edit Add block respectively The latter option allows users to browse through all SIMSIDES library models This way clicking on Edit gt Add blocka new window is displayed where the user can select either ideal or real building blocks by choosing either Add Ideal BlockorAdd Real Block menus respectively In both cases building block models are organized in a set of sublibraries namely integrators quantizers amp comparators D A converters resonators and auxiliary blocks The latter are only available in real libraries Some model libraries are grouped in sublibraries that contain different models corresponding to different kinds of circuit implementations For instance if library Real Integrators is selected a new window is displayed where the user can select the circuit technique CT SC or SI as well as the type of integrator i e either FE or LD in the case of SC and SI integrators and Gm C Gm MC active RC MOSFET C in the case of CT integrators As an illustration Figure 1 3 shows different sublibraries contained in the Real Integrators library A complete list of model libraries and sublibraries is given in Chapter 2 of this user guide Once the NAM block diagram is completed and the different building block model parameters have been defined in the MATLAB workspace the modulator can be simulated in SIMULINK following the same procedure as for the simulation of an arbitrary model in S
17. e thermal noise OTA C CT 2poles OTA C CT 2polesb Input output saturation voltage Finite OTA DC gain nonlinear transconductance two pole dynamic time constant error nonlinear transconductance thermal noise Table 2 6 Gm MC integrator library models in SIMSIDES Model name Circuit effects included Gm MC CTInt 1pole Input output saturation voltage finite OTA DC gain parasitic capacitances one pole dynamic thermal noise Gm MC CTInt 2poles Input output saturation voltage finite OTA DC gain parasitic capacitances two pole dynamic thermal noise Gm l1pole amp Large signal distortion Input output saturation voltage output current limit finite OTA DC gain parasitic capacitances one pole dynamic Gm 2poles amp Large signal distortion Input output saturation voltage output current limit finite OTA DC gain parasitic capacitances two pole dynamic Gm 1pole amp Small Signal Distortion Input output saturation voltage output current limit finite OTA DC gain nonlinear transconductance parasitic capacitances one pole dynamic Gm 2poles amp Small Signal Distortion Input output saturation voltage output current limit finite OTA DC gain nonlinear transconductance parasitic capacitances two pole dynamic 30 SIMSIDES Block Libraries and Models Table 2 7 Active RC integrator library models in SIMSIDES Model name Circuit effects includ
18. e and proceed in a similar way to previous examples in order to compute the SNDR Figure 1 19 shows the results of this analysis by depicting the SNDR versus gm1 Parametric Analysis Considering Two Parameters The Parametric Analysis menu can be used also for implementing parametric analyses considering the variation of two different parameters As an example Figure 1 20 shows the effect of both the OTA transconductance g and the maximum output current J of the front end amplifier on the SNDR of the SAM in Figure 1 15b In order to obtain the graph in Figure 1 20 the following parameters are set up in the Parametric Analysis menu e Parameter name iol which stands for the maximum output current J of the front end integrator 20 SIMSIDES User Guide SNDR vs gm1 110 T T T SNDR dB 0 1 0 2 0 3 0 4 0 5 0 6 0 7 08 0 9 1 gm1 A V x10 Figure 1 19 Using parametric analysis to study the effect of a single model parameter SNDR versus transconductance of the front end amplifier for the SAM in Figure 1 15b e Range vi vf 1e 4 1e 3 N of points 10 Computing Histograms Finally to conclude this example Figure 1 21 illustrates the histograms of the integrators outputs in the front end stage of the modulator in Figure 1 15b These histograms have been obtained by using the Analysis Histograms menu from SIMSIDES and setting up the following model parameters e Name of the signal s to proc
19. e models validated through transistor level electrical simulations and by experimental measurements taken from a number of silicon prototypes have been incorporated into the SIMULINK environment as C MEX S functions This approach drastically increases the computational efficiency in terms of CPU time and accuracy of the simulation results The behavioral models included in SIMSIDES have been compiled and tested in a number of operating systems including Apple OS X UNIX Solaris Linux and Microsoft Windows Both 32 bit and 64 bit system platforms have been successfully tested in the majority of them Although SIMSIDES was originally developed using MATLAB 6 5 and SIMULINK 5 the toolbox has been updated and successfully used in a number of MATLAB SIMULINK versions in the last years This appendix provides a user guide of SIMSIDES giving an overview of the most significant features of the simulator 11 Getting Started Installing and Running SIMSIDES A free copy of SIMSIDES can be downloaded from the following web site http www imse cnm csic es simsides After completing the online registration form and accepting the terms and conditions for using SIMSIDES a zip file named simsides zipis downloaded The following steps must be followed to install the toolbox 1 Uncompress the simsides zip file to a directory of your computer hard disk Let us assume that the directory is named SIMSIDES 2 Start MATLAB program 3 Set the MATLAB
20. e requested parameters i e sampling frequency oversampling ratio etc are set up according to the values given in Figure 1 16 namely SNDR vs Input Amplitude Level T 100r 60 SNDR dB 20 L L L L L L 0 6 5 4 3 2 1 0 10 10 107 10 10 10 10 Ain V Figure 1 18 SNDR versus input amplitude level of the SAM in Figure 1 15b SIMSIDES User Guide 19 e Name of the signal s to process y e Sampling frequency Hz fs e Oversampling ratio M e Input Frequency Hz fi e Window Kaiser e N of Points N e Beta 20 e Kind of Spectrum LP e Figure of merit SNDR After setting up the aforementioned parameters click on Compute and then P1ot to obtain the curve given in Figure 1 18 Parametric Analysis Considering Only One Parameter The Parametric Analysis menu can be used for studying the effect of a given model parameter on the modulator performance For instance let us consider the effect of the OTA transconductance gm of the front end integrator in Figure 1 15b In order to analyze the impact of this parameter on the effective resolution of the modulator go to Parametric Analysis menu and set up the following parameters e Parameter name gm1 Which stands for gm of the front end integrator block in Figure 1 15b e Range vi vf 1e 5 1e 3 N of points 50 e Scale Linear e Analysis SNR SNDR e Second Parameter Off Once these parameters are defined click on Continu
21. ed RC CTInt 1lpole OTA output swing limitation finite OTA DC gain parasitic capacitances capacitance voltage coefficient one pole dynamic thermal noise RC CTInt 2poles OTA output swing limitation finite OTA DC gain parasitic capacitances capacitance voltage coefficient two pole dynamic thermal noise RC 1pole amp Large signal distortion RC 2poles amp Large signal distortion OTA output swing limitation output current limit finite OTA DC gain parasitic capacitances capacitance voltage coefficient one pole dynamic thermal noise OTA output swing limitation output current limit finite OTA DC gain parasitic capacitances capacitance voltage coefficient two pole dynamic thermal noise RC Int 1lin RC Int 2in RC Int 3in Table 2 8 Model name OTA output swing limitation finite OTA DC gain nonlinear trans slew rate parasitic capacitances one pole dynamic thermal noise MOSFET C integrator library models in SIMSIDES Circuit effects included MOSFET C CTInt 1lpole OTA output swing limitation finite OTA DC gain parasitic capacitances capacitance voltage coefficient one pole dynamic thermal noise MOSFET C CTInt 2poles OTA output swing limitation finite OTA DC gain parasitic capacitances capacitance voltage coefficient two pole dynamic thermal noise MOS 1pole amp Large signal distortion OTA output swing limitation out
22. ef description Dig_add_generic_2outs Digital subtraction of a M Level thermometric coded Dig add 3L 5L 13L signal and a M Level thermometric coded signal Dig add 3L 3L 5L 2outs which is scaled by a factor of d The result is a Dig add 3L 3L 7L 2outs M M2 d level thermometric coded digital output Dig add 3L 5L 9L 2outs Dig add 3L 5L 13L 2outs DIGITAL LATCHES Model name Brief description D latch simplest Digital D latches D latch DAC WITH DEM ALGORITHMS Model name Brief description DEM id SD2 Ideal DEM algorithm DAC DEM V04 DAC block with a selectable DEM algorithm There are three options No DEM DWA Pseudo DWA ux SD2 Building block used for sampling an input analog signal by a number of different branches corresponding to the number of DAC unit capacitors SIMSIDES Block Libraries and Models 37 Table 2 15 Error model parameters used in SIMSIDES Auxiliary Blocks Parameter name in alphabetical order Brief description Comparator Input Capacitor C Parasitic capacitance at the comparator quantizer input DEM type DEM algorithm 1 No DEM 2 DWA 3 Pseudo DWA Default 1 Input Capacitor C Input capacitance of the analog adder Nonlinearities of the capacitors Capacitance nonlinear coefficients in an analog adder Number of elements Number of DAC unit elements Output type
23. ess yl y2 Which are the names given to the output of the integrators saved into the MATLAB workspace by using To Workspace blocks from the SIMULINK elementary library e Number of bins 100 1 5 Getting Help SIMSIDES includes a help menu illustrated in Figure 1 22 from which this user guide can be opened by selecting Help User Manual in the SIMSIDES main window In addition a complete list of all behavioral models and their corresponding parameters included in SIMSIDES described in Appendix 2 can be also obtained from this menu by selecting Help Libraries and Models SIMSIDES User Guide 21 SNDR vs gm1 io1 SNDR dB gm1 A V io1 A Figure 1 20 Parametric analysis considering the effect of two parameters gm1 and J 1 on the SNDR 22 SIMSIDES User Guide 2500 2000 a e eo E e e eo Number of Events Number of Events Histogram of the First Integrator Output 0 Signal Amplitude Histogram of the Second Integrator Output T T T 0 Signal Amplitude Figure 1 21 Illustrating the use of histograms of the modulator in Figure 1 15b 800 SIMSIDES File Edit Analysis Optimization User s Manual Libraries and Models About SIMSIDES SIMulink based Simulator IMSE Sigma Delta Design Group CNM CSIC Figure 1 22 Help menu 2 SIMSIDES Block Libraries and Models 2 Overview of SIMSIDES Libraries Table 2 1 compiles all li
24. etc 28 SIMSIDES Block Libraries and Models Table 2 4 Library of SC FE LD resonators included in SIMSIDES Model name Circuit effects included Basic_SC_FE_Res Basic_SC_LD_Res Output swing limitation SC_FE_Res_NonLinear_C Output swing limitation SC_LD_Res_NonLinear_C capacitor nonlinearity SC_FE_Res_Weight_Mismatch Output swing limitation SC_LD_Res_Weight_Mismatch capacitor mismatch SC_FE_Res_Non_Linear_Sampling Output swing limitation SC_LD_Res_Non_Linear_Sampling nonlinear switch on resistance SC_FE_Res_FiniteDCgain Finite OTA DC gain SC_LD_Res_FiniteDCgain output swing limitation parasitic OTA caps SC FE Res FiniteDC amp NonLinearGain Finite nonlinear OTA DC gain SC LD Res FiniteDC amp NonLinearGain output swing limitation parasitic OTA caps SC FE Res Noise OTA thermal noise output swing SC_LD_Res_Noise limitation parasitic load OTA caps SC_FE_Res_Settling Incomplete settling error output swing SC_LD_Res_Settling limitation parasitic load OTA caps SC_FE_Res_All_effects switch on resistance SC_LD_Res_All_effects capacitor nonlinearity and mismatch settling error finite nonlinear DC gain thermal noise parasitic load capacitors SC_FE_Res_All_effects amp NonLinSamp switch nonlinear on resistance SC LD Res All effects amp NonLinSamp capacitor nonlinearity and mismatch 2 4 Real Quantizers amp Comparators Table 2 11 lists the buildin
25. g blocks included in the real Quantizers amp Comparators SIM SIDES library together with a brief description of their operation and main circuit nonideal ities In addition to their ideal parameters additional model parameters are required to model settling error finite nonlinear DC gain thermal noise parasitic load capacitors output swing limitation the different circuit nonidealities These error parameters are listed in Table 2 12 Note that apart from comparators and quantizers there is a building block named Real Sampler which is used for modeling the S amp H circuits that are connected at the input of embedded quantizers in CT ZAMs One of the most critical errors associated to this building block is the clock jitter which is modeled as an uncertainty in the sampling time t corresponding to a stationary process with zero mean and standard deviation defined by the user see Table 2 12 SIMSIDES Block Libraries and Models 29 Table 2 5 Gm C integrator library models in SIMSIDES Model name Circuit effects included Ideal OTA C CTint Ideal Gm C integrator Input saturation voltage nonlinear transconductance Transconductor Output saturation voltage third order intercept point gm no noise new lpole gm Gm C output impedance OTA C CT lpole Input output saturation voltage finite OTA DC gain nonlinear transconductance one pole dynamic time constant error nonlinear transconductanc
26. ging and dropping the models from their corresponding SIMSIDES libraries as illustrated in Figure 1 15a Incorporate the remaining building blocks from the SIMULINK model library To do this go to Edit Simulink Library and drag the required models In this example the following blocks are required Sine Wave and Ground blocks from Sources library Unit Delay and Discrete Filter block from the Discrete library and To Workspace from Sinks library e Finally once all required blocks have been included in the new architecture they are properly connected to implement the required AM architecture shown in Figure 1 15b PO pp 0 2 gt ene 9a y Figure 1 14 Z domain block diagram of a cascade 2 1 DT X AM 14 SIMSIDES User Guide Real Quantizers amp Comparators Ea Real_Multibit_Quantizer Real_Sampler _FE_Int_All_Effects amp NonL Lr T Real Multibit Quantizer for Si Real Comparator Offsel amp Hysteresl EH Real Comparator Offset Hysteresis zr 8r SI Real Multibit Quantizer dig level SDZ 88 To Workspace Cancelation Third Integrator Digital Logic load modelparameters m Only first time Second Integrator Cancelation Logic Models the real SC FE Integrator with every non ideal effect It con
27. gm2 0 87e 3 io2 0 25e 3 ron2 650 Common integrator parameters temp 175 temperature osp 2 7 output swing enll 0 capacitor first order non linear coef enl2 25e 6 capacitor second order non linear coef avnli 0 DC gain first order non linear coef avnl2 15e 2 DC gain second order non linear coef avn13 0 DC gain third order non linear coef avnl4 0 DC gain fourth order non linear coef cparl 0 6e 12 parasitic opamp input capacitance cpar2 0 6e 12 cload 2 28e 12 opamp intrinsic load capacitance Comparators vref 2 DAC reference voltage hys 30e 3 comparator hysteresis Figure 1 16 M file including all model parameters required to simulate the NAM in Figure 1 15b 16 SIMSIDES User Guide Table 1 1 Building block model parameters used for simulating the XAM in Figure 1 15b Building Block Parameter Description Value Variable Input Sine Wave Sine Type Time based Amplitude 0 5 Bias 0 Frequency rad s 2 pi fi Phase rad 0 Sample time 0 Interpret vector parameters Selected First Integrator Integration and Sampling Capacitors Branch 1 Branch 2 Capacitor nonlinear coefficients Weight s variance rms eq input noise temperature OTA DC gain transconductance max output current Positive Negative Output swing Switch on resistance OTA DC gain nonlinear coefs Parasitic capacitances before the OTA Cint1 Cs11 Cs21 cnl1 cnl2 O innoisel temp aol
28. gml iol osp osp roni avnl1 2 3 4 cparl cpar2 Load capacitance cload Positive Input 1 is sampled at phil Sampling Time Ts Identifier for this integrator a Identifier for the next integrator b Second Third Integration and Sampling Capacitors Branch 1 Branch 2 Cint2 Cs12 Cs22 Integrators Capacitor nonlinear coefficients cnl1 cnl2 Weight s variance rms eq input noise temperature 0 innoise2 temp OTA DC gain transconductance max output current ao2 gm2 i02 Positive Negative Output swing osp osp Switch on resistance ron2 OTA DC gain nonlinear coefs avnl1 2 3 4 Parasitic capacitances before the OTA cpar1 cpar2 Load capacitance cload Positive Input 1 is sampled at phil Sampling Time Ts Identifier for this integrator second integrator b Identifier for this integrator third integrator c Identifier for the next integrator c Comparators Vhigh Vlow vref vref Offset Hysteresis 0 hys Phase ON phil Sampling Time Ts Identifier for this quantizer quant1 To Workspace y Variable name y Limit data points to last N Decimation 1 Sample Time Ts Save format Array SIMSIDES User Guide 17 Solver options Type Variable Step Max Step Size Auto Note that integrator building blocks are identified in order to properly compute the equivalent load capacitances required for the incomplete settling error model Computing Output Spectrum The output spectrum of the SAM can be computed in SI
29. gnal bandwidth Capacitor first second order Capacitor first second nonlinearity order nonlinearity Finite and Linear Ron switch on resistance linear model Finite DC Gain of the AO Finite OTA DC gain g switch parameters Finite switch on conductance analytic model Identifier for this integrator Identifier used for settling error model Input Equivalent Thermal Noise OTA input referred thermal noise Input parameters A fi ph switch Amplitude frequency and phase of the sinewave input table look up model Integration Sampling Capacitor Integration sampling capacitors Integration additional load Additional load capacitance at the integration phase Load Capacitor cload Integrator load capacitance Maximum output current Io OTA maximum output current Nonlinearity of the DC Gain OTA DC gain nonlinear coefficients Output Swing Up Down Parasitic Capacitor before the AO Cp Maximum minimum output swing limits Parasitic capacitance at the OTA input pcoef switch parameters nonlinear coefficients of the switch on resistance table look up model Positive Input is Sampled in Input switch clock phase Ron switch on resistance Sampling additional load Additional load capacitance at the sampling phase Sampling Time Clock signal period Switch on resistance Ron Switch on resistance Temp
30. ilable in SIMSIDES including a brief description of the nonidealities considered in each of them The parameters used in these models are the same as those included in SC integrator models listed in Table 2 3 In addition to these parameters the resonator gain can also be defined by the user by setting a parameter named Gain which can be defined in the model dialogue box SIMSIDES Block Libraries and Models 25 Model name Table 2 2 Library of SC FE LD integrators included in SIMSIDES Circuit effects included Basic_SC_FE_Int Basic_SC_LD_Int Output swing limitation SC FE Int Non linear C Output swing limitation SC LD Int Non linear C capacitor nonlinearity SC FE Int Weight Mismatch Output swing limitation SC LD Int Weight Mismatch capacitor mismatch SC FE Int Non Linear Sampling Output swing limitation SC LD Int Non Linear Sampling nonlinear switch on resistance SC FE Int FiniteDCgain Finite OTA DC gain SC LD Int FiniteDCgain output swing limitation parasitic OTA caps SC FE Int Finite amp Non LinearDCGain SC LD Int Finite amp Non LinearDCGain Finite nonlinear OTA DC gain output swing limitation parasitic OTA caps SC FE Int Noise SC LD Int Noise OTA thermal noise output swing limitation parasitic load OTA caps SCOE hh Int Settling SC LD Int Settling Incomplete settling error output swing limitation parasitic load OTA caps
31. ing an existing model SNR SNDR which computes the SNR and or SNDR within the band of interest considering both LP and BP NAMs Harmonic Distortion that computes dynamic harmonic distortion figures like THD and intermodulation distortion figures Histogram used for representing histograms and analyzing the input output swing in XAM building blocks INL DNL which calculates static harmonic distortion MTPR used for computing multi tone power ratio MTPR Parametric Analysis which allows to simulate the impact of a given model parameter on the performance of X AMs Monte Carlo Analysis to do Monte Carlo simulations The required parameters and details involving the aforementioned analysis menus are described below SIMSIDES User Guide 5 ooo SIMSIDES File Edit Analysis Optimization Help Figure 1 3 Illustrating different sublibraries included in the Real Integrators library File Edit Optimization Help Node Spectrum Analysis Integrated Power Noise SNR SNDR Harmonic Distorsion Histogram INL DNL MTPR Parametric Analysis MonteCarlo Analysis Figure 1 4 Analysis menu in SIMSIDES 6 SIMSIDES User Guide Node Spectrum Analysis Figure 1 5a shows the SIMSIDES Node Spectrum Analysis window The following parameters are required to compute the FFT magnitude spectrum Name of the signal s to process where different variable names can be introduced separated by commas These variables c
32. l L3 Users josemdelarosa HOME MATLAB SIMSIDES 2 0 Compilations Linux l 3 Users josemdelarosa HOME MATLAB SIMSIDES 2 0 Compilations Linux l E Users josemdelarosa HOME MATLAB SIMSIDES 2 O Compilations Linux l E Users josemdelarosa HOME MATLAB SIMSIDES 2 O0 Compilations Linux l E Users josemdelarosa HOME MATLAB SIMSIDES 2 O Compilations Linux l E Users josemdelarosa HOME MATLAB SIMSIDES 2 O Compilations Linux l E Users josemdelarosa HOME MATLAB SIMSIDES 2 O Compilations Linux l E Users iosemdelarosa HOME MATLAB SIMSIDES 2 O Comoilations Linux l OMEN Save Close Revert Default a File Edit Analysis Optimization Help O00 File Edit Debug Parallel Desktop Window Help in C 4A B 5 d rY E Q J Users josemdelarosa Desktop v B Shortcuts Z Howto Add 2 What s New gt gt simsides gt gt e b Figure 1 1 Installing and starting SIMSIDES a Setting the MATLAB path b Starting SIMSIDES at the MATLAB prompt 4 SIMSIDES User Guide Edit Analysis Optimization Help New Architecture f Open Architecture X NewSigmaDeltaModulator Exit Edit Analysis Optimization Help New Architecture Open Architecture Directory List SI ES Hybrid DMs ISCAS SIMSIDES exercise UMTS ched current Swit TAMES2 b Figure 1 2 Building and editing SAMs in SIMSIDES a Creating a new SAM architecture b Open
33. own in Figure 1 10 allows to compute MTPR for DMT input signals of different types e Supressing 1 carrier of each 16 i e 1 out of 16 carrier channels are suppressed e Supressing 8 carrier of each 128 ie 8 out of 128 carrier channels are suppressed e Supressing 16 carrier of each 256 i e 16 out of 256 carrier channels are suppressed In addition the following parameters are also needed to compute MTPR e Number of carriers which stands for the number of carrier channels in which the DMT signal is divided e Bins by carrier i e the number of bins assigned to each carrier channel in the FFT File Edit Analysis Optimization Help Y Suppressing 1 carrier of each 16 Figure 1 10 Multi tone power ratio analysis menu SIMSIDES User Guide 11 Histogram Histograms of signals that have been previously saved on the MATLAB workspace can be computed using the HISTOGRAM menu illustrated in Figure 1 11 where the Number of bins specifies the number of intervals in which the signal range will be divided to compute the histogram Parametric Analysis Figure 1 12 shows the SIMSIDES PARAMETRIC ANALYSIS menu This menu is used for analyzing the impact of varying a model parameter on the performance of NAMs Either one parameter or two parameters can be varied simultaneously by selecting the Second Parameter option For each parameter the following data must be specified e Parameter Name i e the name of the model par
34. put current limit finite OTA DC gain parasitic capacitances one pole dynamic thermal noise MOS 2poles amp Large signal distortion OTA output swing limitation output current limit finite OTA DC gain parasitic capacitances two pole dynamic thermal noise SIMSIDES Block Libraries and Models 31 Table 2 9 Gm C resonator library models in SIMSIDES Model name Circuit effects included Ideal_gmC_CT_Resonator gmC_CT_Res_lpole gmC_CT_Res_2poles gmC_CT_Res_2polesfull gmC_CT_Res_lpol larged Ideal Gm C resonator Finite OTA DC gain time constant error one pole dynamic thermal noise Finite OTA DC gain time constant error two pole dynamic thermal noise Input output saturation voltage output current limit finite OTA DC gain time constant error one pole dynamic gmC_CT_Res_2poles_larged Input output saturation voltage output current limit finite OTA DC gain nonlinear transconductance time constant error two pole dynamic gmC_CT_Res_lpole_small larged Input output saturation voltage output current limit finite OTA DC gain nonlinear transconductance time constant error one pole dynamic gmC_CT_Res_2poles_small amp larged Input output saturation voltage output current limit finite OTA DC gain nonlinear transconductance time constant error two pole dynamic 32 SIMSIDES Block Libraries and Models Table 2 10 Gm LC resona
35. ration Figure 1 16 shows the M file used for setting up all model parameters of Figure 1 15 that also includes a brief description of the different parameters and variables included For the sake of completeness Table 1 1 includes the values of all building block parameters as they are described in the SIMSIDES user masks as well as other auxiliary block parameters such as those used in Sine Wave and To Workspace blocks which are required during simulation In addition to these model parameters simulation parameters must be set up to run a simulation To do this goto Simulation Simulation Parameters menu and define the following parameters e Simulation Time Start Time 0 0 Stop Time N 1 Ts SDM parameters Sampling Frequency fs Input Frequency fi Sampling Time Ts OverSampling Ratio OSR M Number of points N fs 5 12e6 fi 5e3 Ts 1 fs M 128 N 65536 Model parameters kt 0 026 1 6e 19 Boltzmann constant First Integrator s parameters Cinti 24e 12 integration capacitor For gain 1 Cs11 6e 12 sampling capacitor branch 1 Cs21 6e 12 sampling capacitor branch 2 innoisel 0 rms value of the input equivalent noise aol 2 63e3 open loop OTA DC gain gml 4 5e 3 transconductance iol 0 977e 3 maximum OTA output current ronliz60 sampling switch on resistance Second and Third Integrators Cint2 3e 12 Cs12 1 5e 12 Cs22 1 5e 12 innoise2 0 ao2 1 38e3
36. ribution with a mean value and a standard deviation which are specified in the analysis menu Different types of probability distributions can be chosen including Normal Log Normal Exponential and Uniform distributions SIMSIDES User Guide 13 1 4 Example This section illustrates the use of SIMSIDES through a simple example in which several kinds of analysis will be carried out to show the main features of the toolbox Figure 1 14 shows the block diagram of the modulator under study which consists of a third order cascade 2 1 DT XAM with single bit quantization in both stages Creating the Cascade 2 1 SAM Block Diagram in SIMSIDES The modulator block diagram shown in Figure 1 14 can be implemented by using the model libraries available in SIMSIDES To this end the same procedure as described in Section 1 2 is followed e Go to SIMSIDES main menu select File New Architecture and introduce a name for the new SAM architecture e Include the integrators and comparators from the SIMSIDES model libraries To do this select Edit Add Block In this example the FE integrators in Figure 1 14 are implemented by using the SC FE Integrator A11 Effects blocks from the Real Integrators library whereas single bit quantizers are modeled by the Real Comparator Offset amp Hysteresis comparator block available in Quantizers amp Comparators library These building blocks can be incorporated in the new architecture by simply drag
37. search path in order to add the SIMSIDES directory To do this go to File menu in MATLAB and select Set Path The Set Path dialog box Extracted from the book CMOS Sigma Delta Converters Practical Design Guide Jos M de la Rosa and Roc o del R o 2013 John Wiley amp Sons Ltd Published 2013 by John Wiley amp Sons Ltd 2 SIMSIDES User Guide opens listing all folders on the search path From this dialog box click the button Add with Subfolders and select the SIMSIDES directory to add to the search path In order to reuse the newly modified search path including SIMSIDES directory and subdirectories click Save and finally click Close This procedure illustrated in Figure 1 1a must be done only the first time SIMSIDES is installed in the hard disk In order to start SIMSIDES type simsides at the MATLAB prompt and the SIMSIDES main window is displayed as illustrated in Figure 1 1b 12 Building and Editing X AM Architectures in SIMSIDES To create anew SAM architecture in SIMSIDES select File and then New Architecture in the main menu and a new SIMULINK model window is displayed Alternatively an existing NAM architecture can be opened by selecting File gt Open Architecture as illustrated in Figure 1 2 In order to define a NAM block diagram in SIMSIDES the required building blocks can be incorporated from the Edit menu as shown in Figure 1 3 Both SIMULINK and SIMSIDES library models can be included by sele
38. siders Non linear Sampling Capacitor Weight Mismatch Output Swing Finite amp Non linear DC gain of the OPAMP Thermal Noise Settling Effect Parameters Capacitors 1 2 order Nonlinearity C2 C11 C12 Cnl1 Cntz ICintl Cs11 6821 cnl1 c2 Weights Variance VRMS eq input T Ron Ivar vrms T ron 0 nnoisel temo ron1 Third Integrator Cancellstio Logic Output Swing Up Down losp ospl AO Finite DC Gain gm Maximun Output Current Av gm lo aol gm ol 1 2 3 4 order nonlinearity DC Gain Anl AvrlZ AvnI3 Avni avnl1avnl2 avni3 aval Parasitic Capacitor before C1 AO Load Capacitor cp1 cp2 cloadi e oat Sampling Time T Activate if you want to evaluate Settling Effect A Activate if there is other integrator conected to its output Identifier for this integrator see help for valid identifier a Identifier for next integrator see help for valid identifier b ER cms 9 om b Figure 1 15 SIMSIDES block diagram of the NAM shown in Figure 1 14 a Building and editing the block diagram b Complete modulator block diagram in SIMSIDES SIMSIDES User Guide 15 Setting Model Parameters The modulator parameters and model parameters required to simulate the block diagram of Figure 1 15 can be either set up in the MATLAB command window or they can be alternatively saved in an M file that is loaded when needed As an illust
39. ss Sampling frequency i e the sampling frequency in Hz Oversampling ratio i e the value of OSR that defines the signal bandwidth in which the IBN is computed e Input frequency Where it is assumed that a single tone input signal is applied e Window Parameters i e the parameters required to defined the window function used for computing the IBN e Kind of Spectrum which specifies the signal nature i e low pass LP or band pass BP After defining all parameters described above the IBN is computed by clicking on the Compute button Harmonic distortion can be also taken into account in the calculation of the IBN by clicking the Include Harmonic in Noise Power button The signal spectrum can be also plotted together with the IBN by choosing the Include Signal Spectrum option SNR SNDR Figure 1 7 shows the SIMSIDES sNR SNDR window The parameters required to calculate the SNR SNDR of a given signal are essentially the same as those used for computing IBN described in the previous section In this case either the SNR or the SNDR is computed 8 SIMSIDES User Guide depending on the Figure of merit selected Note that this kind of analysis calculates the SNR SNDR for a given value of the input signal amplitude If a SNR versus amplitude curve is required a parametric analysis should be chosen as will be described later Harmonic Distortion Figure 1 8 shows the SIMSIDES Harmonic Distortion window which is used for
40. tor library models in SIMSIDES Model name Circuit effects included Ideal_gmLC_CT_Resonator Ideal Gm LC resonator gmLC CT Res 1pole Input output saturation voltage inductance quality factor and series parasitic resistance finite OTA DC gain time constant error one pole dynamic thermal noise gmLC CT Res 2poles Input output saturation voltage inductance quality factor and series parasitic resistance finite OTA DC gain time constant error two pole dynamic thermal noise gmLC l1pole large dist Input output saturation voltage inductance quality factor and series parasitic resistance output current limitation finite OTA DC gain time constant error one pole dynamic thermal noise gmLC 2poles large dist Input output saturation voltage inductance quality factor and series parasitic resistance output current limitation finite OTA DC gain time constant error two pole dynamic thermal noise gm lpole small amp large dist Input output saturation voltage inductance quality factor and series parasitic resistance output current limitation nonlinear transconductance finite OTA DC gain time constant error one pole dynamic thermal noise gmLC 2poles small amp larged Input output saturation voltage inductance quality factor and series parasitic resistance output current limitation nonlinear transconductance finite OTA DC gain time constant error two
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