# HP ADS 1.5 User-defined Models User Manual

Brand: HP, Pages: 216, PDF Size: 1.33 MB

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6-1

Chapter 6: Custom Modeling with

Frequency-Domain Defined Devices

As CAE plays a larger role in the design cycle of RF and microwave circuits and

subsystems, it is important for CAE design systems to satisfy the modeling needs of

the engineer at both the device level and the subsystem level. As communication

applications continue to increase, it is no longer possible to satisfy all modeling needs

with standard, preconfigured models. Thus, Advanced Design System allows users to

define their own nonlinear models, in either the time domain or the frequency

domain.

For working in the time domain, the symbolically defined device (refer to Chapter 5,

Custom Modeling with Symbolically-Defined Devices) enables users to specify

nonlinear models directly on the circuit schematic, using algebraic relationships for

the port voltages and currents. It works very well for creating many nonlinear device

models, but it can be cumbersome for describing the nonlinear, behavioral,

frequency-domain operation of the type of subsystems used in RF and microwave

communication systems.

To address this need, the frequency-domain defined device (FDD) was developed. The

FDD enables you to directly describe current and voltage spectral values in terms of

algebraic relationships of other voltage and current spectral values. This simplifies

development of non-linear, behavioral models that are defined in the frequency

domain. The FDD is ideal for modeling a variety of devices, such as modulators and

demodulators, phase lock loop components, and more.

The FDD includes capabilities that make it well suited for modeling digital

communication subsystems, which often behave in ways that cannot be adequately

modeled as time-invariant. Clocked systems, sampled systems, TDMA pulsed

systems, and digitally-controlled systems are 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 enables you to define trigger

events, to sample the 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.

While the SDD is the user-defined model of choice for modeling at the device and

component level where physics dictates that responses are a function of the

instantaneous port variables, the FDD is preferable for nonlinear, behavioral

modeling in both the frequency and time domains.

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6-2 Signal Models and Sources

Custom Modeling with Frequency-Domain Defined Devices

Before continuing this chapter, you should be familiar with the SDD. This chapter

assumes knowledge of several topics that are presented in the discussion of SDDs,

such as port variables and explicit and implicit equations. For more information,

refer to Chapter 5, Custom Modeling with Symbolically-Defined Devices.

Signal Models and Sources

To fully understand how FDD models work and what they can do, some

understanding of how the simulator models signals in the different simulation

analyses is necessary. While the descriptions that follow use voltages, either voltage

or current signals can be used.

In DC analyses, a node voltage is simply expressed as a constant V for all time. Its

frequency spectrum is simply an impulse at DC with a value of V.

In transient and convolution analyses, a node voltage is still a single variable, but it is

now a time-varying variable V(t), which can theoretically represent any type of signal

from DC up to the Nyquist bandwidth (.5/Tstep). These signals can be periodic,

transient, or random signals. The spectrum of this signal can be computed with

Fourier transform techniques.

In harmonic balance analyses, a node voltage is represented by a discrete spectrum

in the frequency domain. This limits the signal types to quasi-periodic signals, and,

given memory limitations, to a relatively few number of discrete frequencies. The

time-domain waveform can be computed by Fourier transform techniques, based on

the equation below.

The set of harmonic frequencies is defined by the user entering a set of fundamental

frequencies, with an order for each tone. A maximum order parameter is also

required for limiting the number of mixing tones that are included in the set of

harmonic frequencies. For each of these frequencies, each node voltage has a constant

value associated with it, signifying the amplitude and phase of the periodic sinusoid

at that frequency.

Vt()Vkej2pfkt

k0 = N

åèø ç÷

ç÷

æö

real =

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Signal Models and Sources 6-3

These frequencies are referenced by fundamental frequency indices, in the following

manner:

• Given the indices [m,n], the corresponding frequency is m*freq1 + n*freq2,

where freq1 and freq2 are fundamental frequencies.

For example, consider a two-fundamental simulation, with fundamental frequencies

freq1 and freq2 defined as 1GHz and 900 MHz, respectively. The frequency

component at 1 GHz would have indices of [1,0]. The 900 MHz frequency component

would have indices of [0,1]. 100 MHz would have an index of [1,-1], and [2,-1] would

be one of the intermod terms at 1.1 GHz. Note that [0,0] refers to DC. Indices of [-1,1]

reference -100 MHz and its spectral values would be equal to the complex conjugate

of those at 100 MHz.

A three-fundamental frequency system requires three indices [m,n,o] to define a

unique frequency component.

In Circuit Envelope analyses, a node voltage is represented by a time-varying,

frequency-domain spectrum. As in harmonic balance, a set of harmonic frequencies is

user-defined. But here, the spectral amplitude and phase at each of these frequencies

can vary with time, so the signal it represents is no longer limited to a constant

sinusoid. Each of these harmonic frequencies is the center frequency of a spectrum;

the width of each spectrum is ±.5/Tstep. The bandlimited signal within each of these

spectra can contain multiple periodic, transient, or random tones. The actual

time-domain waveform is now represented by the following equation.

Since each time-varying spectrum V

k(t) can be thought of as a modulation waveform

of the center frequency f

k, these are often referred to as envelopes. This does not

imply that there must actually be a frequency component at the center frequency, see

Table 6-1 for examples. Note there are N+1 of these spectra. The one at DC (also

referred to as the baseband component) is limited to a bandwidth of 0.5/Tstep and

must always be real. The other N spectra have a double-sided bandwidth of 1/Tstep

and are usually complex.Vt()V

kt ()ej2pfkt

k0 =N

åèø ç÷

ç÷

æö

real =

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6-4 Signal Models and Sources

Custom Modeling with Frequency-Domain Defined Devices

The envelope waveform Vk(t) has many useful properties. For example, to find the

instantaneous amplitude of the spectrum around f

k at time ts, you simply compute

the magnitude of complex number V

k(ts). 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(ts). Note this is only extracting the magnitude of

the modulation around f

k. It is not including any of the spectral components of

adjacent f

k-1 or fk+1 spectra, even if these spectra actually overlap. If this fk spectrum

has multiple tones inside of it, then this demodulation does include their effects. Table 6-1. Example Signals for Spectrum around f

k

# Formula Description

1V

k=1 Constant cosine cos(2*pi*fk*time)

2V

k=exp(-j*pi/2) or polar(1,-90) or -j Constant sine sin(2*pi*fk*time)

3V

k=A*exp(j*(2*pi*fm*time+B)) One tone (SSB)

A*cos(2*pi*(f

k+fm)*time+B)

4

V

k=A*exp(j*B); freq=1.1 GHz1Same as (3)

(assuming f

k + fm = 1.1 GHz)

5V

k=2*cos(2*pi*fm*time) Two tone (AM suppressed carrier)

6V

k=exp(j*2*pi*fm*time) + exp(-j*2*pi*fm*time) Same as (5)

7

V

k=pulse(time,...); freq=fk+fm1Pulsed RF at a frequency of fk + fm

8Vk= -step(time - delay) A negative cosine wave, gated on at

t=delay

9V

k = (vreal(time)+j*vimag(time))*

exp(j*2*pi*f

m*time)I/Q modulated source centered at

fk+fm. (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 user-defined

randtime functions)

11 V

k=exp(j*2*pi*(-f0 + a0*time/2)*time) Chirped FM signal starting at fk-f0,

rate a0

1.

freq is defined in the paragraph below.

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Signal Models and Sources 6-5

This simple technique does not allow demodulating only one of the tones inside this fk

spectrum and excluding the other tones in the f

k spectrum. To accomplish this, the

desired tone must first be selected by using an appropriate filter in the circuit

simulation. Also note that since the baseband (DC) spectrum represents a real

signal and not a complex envelope, its magnitude corresponds to taking the absolute

value, and its phase is 0 or 180 degrees.

Defining Sources

To define a source for Circuit Envelope, you first identify in which spectral envelope

the signal belongs. This will typically be the fundamental of one of the frequencies

specified in the analysis. Most frequency-domain sources have a single frequency

parameter that can be specified. When these sources are used in a harmonic balance

or Circuit Envelope simulation, the simulator will determine which of the analysis

frequencies is the closest to the source frequency, and if it is close enough, will

internally assign it the corresponding set of indices. A Circuit Envelope simulation

will also determine the frequency offset from the analysis frequency and

automatically shift the signal accordingly. This frequency offset can be up to

±0.5/Timestep. If the source frequency is too far away from any analysis frequency,

then its output is set to 0.0 for that analysis and a warning is generated.

Regarding the equations used to define an output from these sources, instead of

having to define a fundamental frequency and an SSB frequency offset modulation as

in source example 3 in Table 6-1, the simpler format of example 4 is now possible. In

addition, these frequency-defined sources are also directly compatible with simple

transient analysis.