# HP ADS 1.5 User-defined Models User Manual

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

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SDD Examples 5-31

• A weighting function is used in the second SDD equation. It is important to

understand how the weighting function is used by the SDD and is reviewed

here.

• The spectrum for the port voltage _v1 is inverse Fourier transformed into the

time domain.

• The constitutive relation (in this case, -2*C0*sqrt(V0*(V0-vv)) is evaluated

point-by-point in the time domain.

• The resulting waveform (which is the charge for port one) is Fourier

transformed into the frequency domain.

• The weighting function (in this case, jw) is applied in the frequency domain.

The result is the spectrum of the port current _i1.

• When two explicit equations are specified for a single port, the SDD calculates a

spectrum representing the (weighted) result of the first equation, calculates a

spectrum representing the (weighted) result of the second equation, and then

sums the two spectra to get the final spectrum for the port current.

The SDD is simulated in the design TestDiode.dsn. This design uses the diode

capacitance as the C in an RC circuit. It also allows the independent adjustment of

the diode bias voltage. Figure 5-7 shows the frequency response of the RC circuit as

the bias voltage is varied fro -1 to 2 V.

Figure 5-7. Full Varactor Diode Model Results with C

0 = 1 pF, V0 = 0.65V, and a = 0.7

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5-32 SDD Examples

Custom Modeling with Symbolically-Defined Devices

Nonlinear Inductors

A nonlinear current-controlled inductor is defined in terms of its flux-current, or f-i,

relationship

For example, the f-i relationship for a linear two-terminal inductor is

which, when differentiated with respect to time, yields the more familiar inductor

equation

To model a current-controlled nonlinear inductor, differentiate

with respect to time to obtain

which can be rewritten as

This expression can be implemented using an implicit representation. fF

i(). =

f

Li=

vLdi

dt ------

. =

fF

i() =

vd

dt ------Fi () =

vd

dt ------ –Fi ()0. =

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SDD Examples 5-33

For example, the SDD implementation for the nonlinear inductor specified by

is

NoteThis is a good example of a case when using weighting functions with the

implicit representation makes sense.

Obtaining Flux From Inductance

Often the equation for a nonlinear inductor is specified not in terms of flux, but in

terms of a nonlinear inductance L(i) where

Given this representation, the flux function is obtained by integrating the inductance

where we have explicitly included the arbitrary constant of integration f

0.

Fi ()L1iL3i3+ =

vLi()di

dt ------

. =

Fi ()Liˆ

()i ˆ

F0+ d

iò=

### Page 134 from 216

5-34 SDD Examples

Custom Modeling with Symbolically-Defined Devices

Controlling Current, Instantaneous Power

This example is under the Examples directory in the following location:

Tutorials/SDD_Examples_prj/networks/RemCC.dsn

This example illustrates how to use a current as part of an SDD equation, where the

current is from another device in the circuit. For more background on controlling

currents and how to implement them, refer to “Controlling Currents” on page 5-10

and “Defining a Controlling Current” on page 5-15.

In this example, an SDD is used to calculate the instantaneous power dissipated

through resistor R1. The circuit containing R1 is shown here.

Making the power calculation requires both the voltage across R1 and the current

through R1. These values are supplied to the SDD in the following manner:

• The voltage across R1, labeled Vdd, is applied to port 1 of the SDD. Note that

the current at this port is set to zero.

### Page 135 from 216

SDD Examples 5-35

• The current through R1 is specified by using the current through the voltage

source Vdds, and reversing polarity. Recall that only the current through either

a voltage source or current probe can be used as a controlling current. The

instance name of the component is used to specify the controlling current, as

shown in the SDD illustration. In a more complex circuit, you might consider

adding a current probe.

• Although the equation to find power dissipated in R1 is simply Vdd* -_c1, it

must be written in a form that is suitable for the SDD. The first step is to

substitute _v1 for Vdd. Then note that if:

_v2 = -_v1*_c1

and by using an implicit equation, the equation

_v2 + _v1*_c1

can be used to define port 2 of the SDD. Then use a named node (Vpow) to save the

power to the dataset.The graphs of Vdd and the instantaneous power Vpow are

shown below.