Theory of Operation for Circuit Envelope Simulation

The Envelope simulator combines features of time- and frequency-domain representation, offering a fast and complete analysis of complex signals such as digitally modulated RF signals.

Briefly, this simulator permits input waveforms to be represented in the frequency domain as RF carriers, with modulation "envelopes" that are represented in the time domain as shown in the following figure.


Modulated signal in the time domain

The following concepts present a basic overview of the circuit envelope simulation process.

To describe the circuit envelope simulation process more specifically, in an envelope simulation each node voltage is represented by a discrete spectrum having time-varying Fourier coefficients. The set of spectral frequencies is user-defined; the amplitude and phase at each spectral frequency can vary with time, so the signal representing the harmonic is no longer limited to a constant, as it is with harmonic balance. Each spectral frequency can be thought of as the center frequency of a spectrum; the width of each spectrum is ±0.5/Time step. The following figure illustrates this, where the minimum envelope bandwidth is equal to the bandwidth of the modulation signal. In most cases the bandwidth of the modulation signal is much smaller than the lowest user-defined spectral frequency (which corresponds to the "carrier" frequency), unlike what is shown in the figure.


Spectra in the frequency domain

The bandlimited signal within each spectrum can contain periodic, transient, or random tones. The actual time-domain waveform is represented as a sum of carriers (with harmonics and intermodulation products), where each envelope can vary with time:

Here, v(t) is a voltage at any node in the circuit, including the input. The Fourier coefficients, V k (t), are allowed to vary with time and may represent an arbitrary modulation of each carrier. Since each time-varying spectrum V k (t) can be thought of as a modulation waveform with a center frequency f k , these are often referred to as "envelopes." This spectrum may represent transient signals with continuous spectra, such as a digital modulation envelope over an RF carrier, or periodic signals with discrete spectral lines, such as the two RF tones required for intermodulation distortion analysis.

The following figure illustrates a modulated signal and the time-varying spectrum that results from the simulation. Any spectral component obtained from the simulation can be processed and displayed in amplitude, phase, I (the in-phase modulation component), or Q (the quadrature modulation component). By computing the Fourier transform of the spectral component, the simulator can present the spectrum around the component, as in a spectrum analyzer display.


A Modulated signal and its simulated time-varying spectrum

This simulator does not require that a spectral component be present at the center frequency. The following table gives examples of how the spectrum can be defined. You can use a V_1Tone source component to generate the various signals depicted in the table, assigning to the source parameter V the various expressions for V k . In a given envelope simulation, there are N + 1 possible spectral components. The one at DC (also referred to as the baseband component) is limited to a bandwidth of 0.5/Time step , and only the real portion of V k is used. The other N spectra have a double-sided bandwidth of 1/ Time step and are usually complex, as shown in the figure Spectra in the frequency domain.

The envelope waveform V k(t) has many useful properties. For example, to find the instantaneous amplitude of the signal around f k at time t s, simply compute the magnitude of the complex number V k (t s ). Similarly, the phase, real, and imaginary values of instantaneous modulation can be extracted by simply computing the phase, real, and imaginary values of V k (t s ).

Note
This process only extracts the magnitude of the modulation around f k . It does not include any of the spectral components of adjacent f k-1 or f k+1 spectra, even if these spectra actually overlap. If this f k spectrum has multiple tones inside of it, then this demodulation does include their effects.


Examples of Defining a Spectrum Around f k
# Formula that specifies the envelope Description of the signal in the time domain
1 V k =1 Pure cosine: cos(2*pi*f k *time)
2 V k =exp(j*pi/2) or polar(1,90) or 1*j Pure sine: sin(2*pi*f k *time)
3 V k =A*exp(j*2*pi*f m *time+B) One tone (SSB) A*cos(2*pi*(f k +f m )*time+B)
4 V k =A*exp(j*B); freq=1.1 GHz Same as (3) (assuming f k + f m = 1.1 GHz)
5 V k =2*cos(2*pi*f m *time) Two tones (AM suppressed carrier)
6 V k =exp(j*2*pi*f m *time) + exp(-j*2*pi*f m *time) Same as (5)
7 V k =pulse(time,...); freq=fk+fm Pulsed RF at a frequency of f k + f m
8 V k = −step(time − delay) A negative cosine wave, gated on at t=delay
9 V k = (vreal(time)+j*vimag(time))*exp(j*2*pi*f m*time) I/Q modulated source centered at f k +f m . (vreal(), vimag() user-defined functions)
10 V k =(1 + vr1) * exp(j*2*pi*vr2) Amplitude- and noise-modulated source at f k. (vr1, vr2 are user-defined randtime functions, not available in Release 1.0)
11 V k =exp(j*2*pi*(-f 0 + a 0 *time/2)*time) Chirped FM signal starting at f k - f 0 , rate = a 0

This simple technique does not allow the demodulation of only one of the tones inside this f k spectrum and the exclusion of the others. To demodulate only one tone, first select the desired tone by using an appropriate filter in the circuit to be simulated. Also, note that because the baseband (DC) spectrum represents a real signal and not a complex envelope, its magnitude corresponds to taking the absolute value of that signal, and its phase is either 0 or 180 degrees.

Circuit Envelope and Frequency-Domain-Defined Devices

As the applications for wireless communications continue to grow, it is no longer possible to satisfy all modeling needs with standard, preconfigured models. Users need methods to define their own nonlinear models in either the time or the frequency domain. The frequency-domain-defined device (FDD) has been developed to allow a user to describe current and voltage spectral values directly, in terms of the algebraic relationships of other voltage and current spectral values.

Another trend in digital communication systems is the issue of timing, since it is increasingly common to encounter subsystems that behave in ways that cannot be modeled as time-invariant. Clocked systems, sampled systems, TDMA pulsed systems, and digitally controlled systems are all becoming more common, even in the RF and microwave area, and behavioral models must be able to include these effects. So, in addition to its frequency-domain modeling attributes, the FDD also allows the modeler to define trigger events, to sample voltages and currents at trigger events, and to generate outputs that are arbitrary functions of either the time of the trigger or of the complex spectral voltage and current values at these trigger events.

Circuit Envelope and Components

In general, any of the components available in Advanced Design System can be used in circuits where envelope simulations are performed. Some components lend themselves especially well to such circuit designs, such as n-state modulators and demodulators or spectral waveform sources.

Using Functions and Equations

Functions and equations can be placed in a schematic in the same manner as ADS components, and some are especially well-suited to envelope simulations and behavioral model designs. There is also a set of functions that can be used only with FDDs, and a set of variables that can be used only with SDDs; they, too, can facilitate digital communication designs where the envelope simulator is applied.

To use the Variables and equations component:

  1. From the Data Items palette, select Var eqn (Variables and equations) and place it in the Schematic window.
  2. Edit it and select the File Based option from the Variable or Equation Entry Mode drop-down list.
  3. In the Data Access Component field, type the Instance Name – or select it from the drop-down list – of the DAC that points to the file containing the data of interest.
    This makes it possible to use lists of data as component parameter values. Such data can also be used with n-state components to define the phase and amplitude of the various states. These components are especially efficient in envelope simulations, and dataset and list arrays simplify the entering of strings of data as parameter values.

Automatic Verification Modeling

Automatic Verification Modeling (AVM) is a user-selected mode of operation that can significantly speed up formerly lengthy cosimulations of Analog/RF circuits. This mode is also known as Fast Cosimulation. When this mode is enabled, the analog subcircuit is first characterized using a variety of Harmonic Balance simulations at the start of every Ptolemy simulation. Then during the actual Ptolemy simulation, this characterization data is used to predict the response of the subcircuit instead of performing the full circuit simulation at each time point.

Since this characterization is normally done at the start of every Ptolemy sweep based on the full circuit level schematic, the overall capability is basically the same as if the actual circuit level representation is used throughout the cosimulation. For example, optimization of circuit level parameters, or swept parameters including bias, temperature or swept carrier frequency will continue to operate as expected. These capabilities do not exist when the circuit is manually replaced with behavioral models.

This ability to predict the modulated response based on the Harmonic Balance characterization relies on the fact that many circuits, when used in relatively narrow band modulated applications, can have their nonlinearity represented as a static nonlinearity that is strictly a function of the instantaneous amplitude of the carrier. Many of these circuits, such as amplifiers and mixers, have little, if any, frequency response over the modulation bandwidth of interest. Any frequency response effects that do exist can then often be represented as either a linear filter on either the input or the output of the nonlinearity.

Each output of the Analog/RF subcircuit is then characterized by the following equation:

The functions are determined by the swept amplitude Harmonic Balance simulation. The HarmGain is the harmonic gain determined from the harmonic indices of the input and output frequencies.

If phase characterization has been enabled, by setting the "Num. of phase pts" parameter to a non-zero value, then each output is characterized by this modified equation:

In this case, functions are determined by a two dimensional swept amplitude and swept phase Harmonic Balance simulation.

If the subcircuit nonlinearities are a function the input phase, as in a nonlinear IQ demodulator, then the amplitude only characterization is not accurate and the two dimensional amplitude and phase characterization must be used. However, if the IQ Modem phase characteristics are linear, then the IQ input or output pair can be identified in the Node Names section, and the Magnitude only characterization can still be used, as the HarmGain value is then set to 1. This requires that the I/Q pair be properly identified such that there are no phase inversions introduced, since this would require a harmonic gain of -1.

Note that the magnitude only characterization assumes the output phase can be determined from the harmonic indices of the input and output frequencies. In certain rare cases, this can be ambiguous. For example, if the input frequency is fund1 and the output frequency is 2*fund1 , then the simulator assumes the output signal is generated by a doubling the input frequency and so the input phase is doubled. However, if this 2*fund1 output frequency is actually generated by mixing with another LO source at the fund1 frequency and so the phase relationship is supposed to be linear, then the AVM (Fast Cosim) results will be incorrect. If the mixer LO is operating at an independent fund2 frequency, with a mixer output at fund1 + fund2, then the HarmGain of 1.0 is correctly determined. So, as with the IQ demodulator, if there are circuit sources operating at the same frequency as the input signal, then caution should be used when enabling this AVM (Fast Cosim) mode, and the two dimensional amplitude and phase characterization may be required.

In addition to the swept amplitude characterization, the AVM characterization also includes a small signal Harmonic Balance frequency sweep. In this case, the input amplitude is set to 0, and the small signal frequency is swept between ±0.5/ TimeStep . Note that even though the input amplitude is set to 0, a nonlinear analysis is still being done so any frequency translation effects due to internal mixers will be fully captured. An impulse response representing this frequency response can then be generated, and then, as the user's choice, placed on either the input or the output of the nonlinear block. An additional delay can also be added to the frequency response, so that the impulse can be made a more accurate representation of the frequency response. The user should set the number of frequency points high enough that any frequency response deviations are sufficiently sampled (a minimum of 4 samples every 360 degrees). The maximum duration of the impulse response will be about 0.75/ FreqSpacing, where

N is determined so that 2 N is just larger than the user-specified number of frequency points. So, if frequency compensation is needed, the number of frequency points should generally be greater than the maximum impulse response time of the circuit around the carrier frequency plus any additional Delay specified in the Cosim Implementation block, both normalized by the Circuit Envelope TimeStep value.

In addition to the amplitude and frequency response characterization, nonlinear noise characterization is also done. A single value for the equivalent input noise for each output is determined and then added to the input signal prior to the above nonlinear and frequency response effects. In the case of multiple outputs, these equivalent noise sources are uncorrelated. So any correlation of the Analog/RF subcircuit added noise between multiple outputs is lost during this AVM (Fast Cosim) mode. Whether or not this noise characterization is done and implemented is determined by the standard EnvNoise parameter set in the Envelope simulation. Normally, the frequency points used for noise characterization are the same as for small-signal response characterization in which a linear frequency sweep is used. Such a linear frequency sweep may require too many frequency points to properly capture narrow band noise such as 1/f noise. To handle 1/f noise characterization efficiently you can choose to set an independent log sweep.

In certain cases, the time spent doing this characterization can be eliminated if the user requests that the simulator use previous characterization. Once this mode is selected, then it is the responsibility of the user to make sure that the previous characterization is still valid, and that circuit parameters have not been changed, perhaps by optimization, biases have not changed, carrier frequencies have not changed, etc. The circuit should not have changed its connectivity within the Ptolemy environment and names of the OutputSelectors cannot have changed either. Also, the format and data in the dataset must be in the same expected configuration as when it was written by simulator.

In addition to the characterization and implementation portion of the AVM (Fast Cosim) mode, there is also a user selectable verification step. If the user specifies a non-zero verification Stop Time, then the normal Circuit Envelope simulation is performed in parallel with the fast cosimulation predictions. The error over this verification is then computed and output to determine how well these predictions are performing. If the behavior is unacceptable, as determined by the Accept Tolerance, then the AVM (Fast Cosim) will be disabled and only the normal Circuit Envelope results will be used. Clearly, if used, this verification time should be set long enough to include a representative portion of the input signal. This may need to take into account the fact that many sources, due to channel filtering, take a while to generate their full amplitude outputs.

AVM Limitations

Though you may have selected the AVM (Fast Cosim) mode, it may be disabled for the following reasons:

Additional limitations of the AVM (Fast Cosim) mode, that may not be automatically detected by the simulator unless verification is enabled, include:

 

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