Periodic AC Analysis (pac)
Description
The periodic AC (PAC) analysis is used to compute transfer functions for circuits that exhibit frequency translation. Such circuits include mixers, switched-capacitor filters, samplers, phase-locked loops, and the like. PAC is a small-signal analysis similar to AC analysis, except that the circuit is first linearized about a periodically varying operating point as opposed to a simple DC operating point. Linearizing about a periodically time-varying operating point allows transfer-functions that include frequency translation, which is not the case when linearizing about a DC operating point because linear time-invariant circuits do not exhibit frequency translation. In addition, the frequency of the sinusoidal stimulus is not constrained by the period of the large periodic solution.
Computing the small-signal response of a periodically varying circuit is a two-step process. First, the small stimulus is ignored and the periodic steady-state response of the circuit to possibly large periodic stimulus is computed using PSS analysis. As part of the PSS analysis, the periodically time-varying representation of the circuit is computed and saved for later use. The second step is to apply the small stimulus to the periodically varying linear representation to compute the small signal response. This is done using the PAC analysis. A PAC analysis cannot be used alone, it must follow a PSS analysis. However, any number of periodic small-signal analyses such as PAC, PSP, PXF, and PNoise, can follow a PSS analysis.
Modulated small signal measurements are possible by using Analog Design Environment (ADE) environment. The modulated option for PAC and the other modulated parameters are set by the Analog Design Environment (ADE). PAC analyses with this option produces results that could have limited use outside such an environment. Direct Plot is configured to analyze these results and combine several wave forms to measure AM and PM response due to single sideband or modulated stimuli. For details, see the SpectreRF User Guide.
Unlike AC analysis, PAC analysis can print the time - domain simulation results by specifying the outputperiod parameter. In addition, unlike other analyses in Spectre, this analysis can only sweep frequency.
Unlike other analyses in Spectre, this analysis can only sweep frequency.
Syntax
Name ... pac parameter=value ...
Parameters
Sweep interval parameters
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start
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0
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Start sweep limit.
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stop
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Stop sweep limit.
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center
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Center of sweep.
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span
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0
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Sweep limit span.
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step
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Step size, linear sweep.
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lin
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50
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Number of steps, linear sweep.
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dec
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Points per decade.
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log
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50
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Number of steps, log sweep.
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values
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[...]
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Array of sweep values.
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valuesfile
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Name of the file containing the sweep values.
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sweeptype
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unspecified
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Specifies if the sweep frequency range is the absolute frequency of input or if it is relative to the port harmonics. When the unspecified value is used, Spectre RF sweeps using relative when autonomous simulation is performed or when the analysis is PSP; for other cases Spectre RF sweeps the absolute value of the input. Possible values are absolute, relative and unspecified.
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relharmnum
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1
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Harmonic to which relative frequency sweep should be referenced.
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Sampled analysis parameters
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ptvtype
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timeaveraged
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Specifies whether the PTV analysis will be traditional or sampled under certain conditions. Possible values are timeaveraged and sampled.
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sampleprobe
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The crossing event at this port triggers the sampled small signal computation.
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thresholdvalue
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0
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Sampled measurement is done when the signal crosses this value.
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crossingdirection
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all
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Specifies the transitions for which sampling must be done. Possible values are all, rise, fall and ignore.
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maxsamples
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16
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Maximum number of sampled events to be processed during the sampled analysis.
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extrasampletimepoints
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[...]
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Additional time points for sampled PTV analysis.
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Output parameters
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sidebands
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[...]
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Array of relevant sidebands for the analysis.
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maxsideband
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7
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An alternative to the sidebands array specification, which automatically generates the array: [ -maxsideband ... 0 ... +maxsideband ]. For the shooting analysis, the default value is 7. For HB small signal analysis, the default value is the harms/maxharms setting in the HB large signal analysis. It is ignored in HB small signal when it is larger than the harms/maxharms value of large signal.
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freqaxis
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Specifies whether the results should be printed as per the input frequency, the output frequency, or the absolute value of the output frequency. Default is absout. . Possible values are absout, out and in.
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save
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Signals to output. Possible values are all, lvl, allpub, lvlpub, selected, none and nooutput.
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nestlvl
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Levels of subcircuits to output.
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outputperiod
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0.0 (no output)
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Time-domain output period. The time-domain small-signal response is computed for the period specified, rounded to the nearest integer multiple of the pss period.
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Convergence parameters
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tolerance
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Tolerance for linear solver. The default value is 1.0e-9 for shooting-based solver and 1.0e-4 for harmonic balance-based solver.
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relativeTol
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Relative tolerance for harmonic balance-based linear solver. Default value is 1.0e-2.
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gear_order
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2
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Gear order used for small-signal integration.
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solver
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turbo
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Solver type. Possible values are std, turbo, std_hh and turbo_hh.
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oscsolver
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turbo
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Oscillator solver type. It is recommended that you use ira for huge circuits. Possible values are std, turbo, ira and direct.
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resgmrescycle
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short
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Restarts GMRES cycle. Possible values are instant, short, long, recycleinstant, recycleshort, recyclelong and custom.
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hbprecond_solver
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autoset
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Select a linear solver for the GMRES preconditioner. Default is autoset. With autoset, the simulator will automatically select the appropriate precondtioner. The preconditioner affects the rate of convergence of the linear matrix solver used in periodic small-signal analysis. When autoset is selected, the simulator may decide to switch to a different preconditioner after the analysis begins. When that happens, the simulator may issue a warning instructing you to choose a different preconditioner during subsequent runs. Although not required, choosing a different preconditioner according to the simulator's instructions may speed up subsequent analyses. Possible values are basicsolver, blocksolver, autoset, blockdense, blocksolver2 and directsolver.
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lowmem
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0
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Harmonic balance low memory mode; Possible values are 0, 1, or number (>=10). The default value is '0', the low memory mode is turned off; if '1' is set, the standard low memory mode is turned on; If a number no less than 10 is set, Spectre interprets the value as the memory requested in GigaBytes..
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krylov_size
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200
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This parameter is used to set maximum iteration count of the linear matrix solver used in periodic small-signal analysis. After reaching 1.25*krylov_size iterations, the iteration is forced to terminate because of the poor rate of convergence. Increase the krylov_size if the simulation reports insufficient norm reduction errors in GMRES.
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osc_version
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dts
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Specifies the method to use in small signal analysis for autonomous circuit. Possible values are floquet, augmented and dts.
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osc_accuracy
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2
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Accuracy control in small signal analysis for autonomous circuit when osc_version=dts. The higher this value, the more iterations GMRES solver will take. Maximum effective value is 5.
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freqdivide
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1
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Large signal frequency division. Used for oscillator circuit with divider in when osc_version=dts for shooting engine.
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Annotation parameters
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annotate
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sweep
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Degree of annotation. Possible values are no, title, sweep, status, steps and detailed_hb.
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title
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Analysis title.
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Modulation conversion parameters
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modulated
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no
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Compute transfer functions/conversion between modulated sources and outputs. Possible values are single, first, second and no.
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inmodharmnum
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1
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Harmonic value for the input source modulation.
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outmodharmvec
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[...]
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Harmonic list for the output modulations.
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moduppersideband
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1
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Index of the upper sideband included in the modulation of an output for PAC and HBAC, or an input for PXF.
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modsource
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Refer the output noise to this component.
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Rapid distortion analysis parameters
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perturbation
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linear
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The type of PAC analysis. The default is linear for normal PAC analysis. im2ds stands for im2 distortion summary and ds stands for distortion summary. Triple beat analysis is not supported for shooting engine, PSS must be run before PAC with 'flexbalance=yes' or 'harmonicbalance=yes'. Value multiple_beat is deprecated and will be removed in the future: use triple_beat instead. Possible values are linear, ds, ip3, ip2, im2ds, multiple_beat and triple_beat.
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flin_out
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0 Hz
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Frequency of linear output signal.
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fim_out
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0 Hz
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Frequency of IM output signal.
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out1
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NULL
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Output signal 1.
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out2
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NULL
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Output signal 2.
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contriblist
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NULL
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Array of device names for distortion summary. When contriblist=[""], distortion from each non-linear device is calculated.
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maxharm_nonlin
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4
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Maximum harmonics of input signal frequency induced by non-linear effect.
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rfmag
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0
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RF source magnitude.
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rfdbm
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0
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RF source dBm.
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rf1_src
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NULL
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Array of RF1 source names for IP3/IP2/IM2.
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rf2_src
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NULL
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Array of RF2 source names for IP3/IP2/IM2.
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rf_src
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NULL
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Array of RF source names for triple beat analysis, triple beat is not supported in shooting engine, PSS must be run before PAC with 'flexbalance=yes' or 'harmonicbalance=yes'.
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freqs
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NULL
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Array of RF source frequencies for triple beat analysis, triple beat is not supported in shooting engine, PSS must be run before PAC with 'flexbalance=yes' or 'harmonicbalance=yes'.
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rfampls
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NULL
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RF source amplitudes; the units are dBm for ports, Voltage for v-sources and Ampere for i-sources.
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You can select the set of periodic small-signal output frequencies of interest by setting either the maxsideband or the sidebands parameters. For a given set of n integer numbers representing sidebands K1, K2, ... Kn, the output frequency at each sideband is computed as f(out)= f(in) + Ki * fund(pss), where f(in) represent the (possibly swept) input frequency, and fund(pss) represents the fundamental frequency used in the corresponding PSS analysis. Therefore, when analyzing a down-converting mixer, while sweeping the RF input frequency, the most relevant sideband for IF output is Ki= -1. When simulating an up-converting mixer, while sweeping IF input frequency, the most relevant sideband for RF output is Ki= 1. By setting the maxsideband value to Kmax, all 2 * Kmax + 1 sidebands from -Kmax to +Kmax are generated.
The number of requested sidebands does not change substantially the simulation time. However, the maxacfreq of the corresponding PSS analysis should be set to guarantee that | max{f(out)} | is less than maxacfreq; otherwise, the computed solution might be contaminated by aliasing effects. The PAC simulation is not executed for | f(in) | greater than maxacfreq. Diagnostic messages are printed for those extreme cases, indicating how maxacfreq should be set in the PSS analysis. In majority of the simulations, however, this is not an issue, because maxacfreq is never allowed to be smaller than 40x the PSS fundamental.
With PAC, the frequency of the stimulus and of the response are usually different (this is an important area in which PAC differs from AC). The freqaxis parameter is used to specify whether the results should be output versus the input frequency (in), the output frequency (out), or the absolute value of the output frequency (absout).
You can define sweep limits by specifying the end points or by providing the center value and span of the sweep. Steps can be linear or logarithmic, and you can specify the number of steps or the size of each step. In addition, You can specify a step size parameter (step, lin, log, or dec) to determine whether the sweep is linear or logarithmic. If you do not specify a step size parameter, the sweep is linear when the ratio of stop to start values is less than 10 and logarithmic when this ratio is 10 or greater. Alternatively, you may specify the values that the sweep parameter should take by using the values parameter. If you specify both a specific set of values and a set specified using a sweep range, the two sets are merged and collated before being used. All frequencies are in Hertz.
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