# 10.6.3. A closer look at analyses and performance measures¶

In this section we are going to take a closer look at analyses and performance measures we defined in the common part of the problem definition.

Analysis op is an operating point analysis. No special arguments are specified in the command string (op()) because this analysis has none. The amplifier definition def and the top-level circuit tb are included in the simulator’s input netlist. Four performance measures are extracted from operating point analysis results:

• isup is the current supplied by the power supply. It is extracted with a simple scipt isup=-i('vdd').

• out_op is the output voltage operating point. The extraction is pefromed by an expression v('out'). One could also write a script (out_op=v('out')) or a script (__result=v('out')).

• vgs_drv is the Vgs overdrive voltage (i.e. how much above the threshold is the operating point Vgs voltage of a transistor. The result of this measurement is a vector with as many entries as there are transistors defined in variable mosList. The script is written with comments and is self-explanatory.

• vds_drv is the Vds overdrive voltage (i.e. how much above the boundary of the saturation is the operating point Vds voltage). The script is similar to the vgs_drv script.

The dc analysis sweeps the input voltage source Vin1 from -2V to 2V with 100 uniform (linearly spaced) steps. The amplifier definition def and the top-level circuit tb are included in the simulator’s input netlist. The circuit has a feedback loop comprising R1 and R2. Due to this feedback the operating point (where Vin1 is 0V) is in the middle of the amplifier’s active region. Sweeping Vin1 from -2V to 2V results in the output going from positive saturation across the active region into the negative saturation. If we observe the output voltage against the input voltage between the amplifier’s non-inverting (inp) and inverting input (inn) we get the amplifier’ DC characteristic for differential gain. By computing the derivative of y wrt. x in this graph we get the dependence of the gain on the input differential voltage. This dependence is a bell shaped curve. One desires the bell to be as wide as possible. We express the width of the curve with the swing perfromance measure which computes the equivalent output voltage range width where the gain is above 50% of the maximal gain.

The ac analysis sweeps the frequency from 1Hz to 1Thz logarithmically with 10 points per decade. The analysis includes the amplifier definition def and the top-level circuit tb in the simulator’s input netlist. The AC excitation comes from the Vin1 input voltage source whose ac parameter is set to 1.

Its results are used for computing

• differential gain (gain) which is obtained as the magnitude of the ratio between output and input differential voltage obtained with expression m.ACmag(m.ACtf(v('out'), v('inp', 'inn'))). Because the expression results in a vector holding the values of gain for all simulated frequency points we extract the first component which corresponds to gain at 1Hz.

• unit-gain bandwidth (ugbw) which is the frequency where the differential gain becomes 1. It is computed with expression m.ACugbw(m.ACtf(v('out'), v('inp', 'inn')), scale()). The expression uses the frequency scale to compute the value of ugbw.

• Phase margin (pm) is the difference in phase between -180 degrees and the phase at unity-gain. It is computed with expression m.ACphaseMargin(m.ACtf(v('out'), v('inp', 'inn'))).

Three additional ac analyses (accom, acvdd, and acvss) are produce the waveforms from which the gains from Vdd1, Vss1, and Vcom to the circuit’s output. All of them use the tbrr top level circuit instead of tb. They differ only in the AC excitation which is selected by three netlist parameters: accom, acvdd, and acvss. Their frequency scales are indetical to that of the ac analysis so that the frequency response of the CMRR, PSSR_VDD, and PSRR_VSS can be computed by dividing the respective gain vectors. The following performance measures are computed

• From accom analysis gain_com (common mode gain at 1Hz) which is obtained as m.ACmag(m.ACtf(v('out'), 1.0))[0]. Note that the input signal is equal to 1 (due to the ac parameter of the Vcom voltage source (which is set by the accom netlist parameter.

• From acvdd analysis gain_vdd (gain from Vdd to output at 1Hz).

• From acvss analysis gain_vss (gain from Vdd to output at 1Hz).

Noise analysis names noise sweeps the frequency across the same scale as the ac analysis. It uses the tb top level circuit. and computes the output noise at the amplifier’s output and the equivalent input noise at Vin1. The following performance measures are computed from its results:

• Output noise power spectrum density at 1kHz onoise1k which is computed with expression m.XatI(ns('output'), m.IatXval(scale(), 1e3)[0]) The function m.IatXval finds the position in the frequency scale that corresponds to 1kHz. The obtained position is used for extracting the noise spectral density from the output noise spectrum.

• Equivalent input noise power spectrum density at 1kHz inoise1k which is computed with expression m.XatI(ns('input'), m.IatXval(scale(), 1e3)[0]) The function m.IatXval finds the position in the frequency scale that corresponds to 1kHz. The obtained position is used for extracting the noise spectral density from the equivalent input noise spectrum.

• The contribution of Mn2’s channel noise to the equivalent input power spectrum density at 1kHz (in1kmn2id) computed as m.XatI(ns('input', ipath('xmn2', 'x1', 'm0'), 'id'), m.IatXval(scale(), 1e3)[0]) The ipath function is used for constructing the fully qualified instance name of the built-in MOS instance corresponding to Mn2.

• The contribution of Mn2’s drain resistance thermal noise to the equivalent input power spectrum density at 1kHz (in1kmn2rd) computed as m.XatI(ns('input', ipath('xmn2', 'x1', 'm0'), 'id'), m.IatXval(scale(), 1e3)[0])

• The total contribution of Mn2’s noise to the equivalent input power spectrum density at 1kHz. (in1kmn2) computed as m.XatI(ns('input', ipath('xmn2', 'x1', 'm0')), m.IatXval(scale(), 1e3)[0])

Transient analysis tran uses the tb top level circuit and computes the response to a pulse generated by Vin1. The pulse initial level (lev1), pulse level (lev2), start time (tstart), rise time (tr), fall time (tf), and width (pw) are specified in the heads variable (see previous section). The pulse rises from lev1 to lev2 and then drops down back to lev1. Because the top level circuit is an inverting amplifier the amplifier’s output first falls and then rises again. The following performance measures are computed from the resulting waveforms.

• undershoot at falling edge of the amplifier’s output (overshdn). Expression m.Tundershoot(v('out'), scale(), t1=param['tstart'], t2=(param['pw']+param['tstart']+param['tr'])) is used. Arguments t1 and t2 specify the time window within which the undershoot happens (between t=tstart and t=tstart+tr+pw). The reference signal levels are taken at both ends of the specified time window.

• oveshoot at rising edge of the amplifier’s output (overshup). The m.Tovershoot function is used in the expression on time window between t=tstart+tr+pw and the end of the waveform.

• settling time at the falling edge of amplifier’s output (tsetdn) computed with expression m.TsettlingTime(v('out'), scale(), t1=param['tstart'], t2=(param['pw']+param['tstart']+param['tr']))

• settling time at the rising edge of amplifier’s output (tsetup)

Transient analysis translew also uses the tb top level circuit. It is identical to tran analysis with one exception. The initial level and the pulse level are chosen in such manner that the amplifier’s output reaches saturation level. Two performance measures are obtained from the resulting waveforms

• The falling slew rate slewdn is observed within the time window between t=tstart and t=tstart+tr+pw. It is compunted with expression m.TslewRate('falling', v('out'), scale(), t1=param['tstart'], t2=(param['pw']+param['tstart']+param['tr']))

• The rising slew rate slewup is observed within the time window between t=tstart+tr+pw and waveform end. The expression is similar to the one used for computing slewdn.

Certain performance measures are not computed from analysis results. They all use the results of analysis named blank. The command for this analysis is set to None so the simulator is not invoked. The values of these measures are computed from previously evaluated performance measures, netlist parameters, and user-defined variables. A netlist parameter named diff_w can be accessed as param['diff_w']. Variables are accessed by their names. The results of performance measures that were computed from analysis results are accessed as result[measure_name][corner_name]. The variable cornerName holds the name of the corner for which the performance measure is being evaluated.

• area is the approximate circuit area. It is computed from netlist parameters that specify device dimensions.

• cmrr is the common mode rejection ratio computed from gain and gain_com. Because both gains are in decibels, CMRR is computed with a simple subtraction. result['gain'][cornerName]-result['gain_com'][cornerName]

• psrr_vdd is the power supply rejection ratio of the Vdd power supply.

• psrr_vss is the power supply rejection ratio of the Vss power supply.