# 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 copmmon 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. Their
value depends on 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.