# HP ADS 1.5 User-defined Models User Manual

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

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SDD Examples 5-21

Current through the input resistance Ri can be expressed as:

You could use this equation directly as the equation for port 1, but then it would be

impossible to set R

i= . So, rewrite the explicit equation for port 1 using input

conductance G

i instead:

For port 2, the non-zero output resistance R

o is included in the model by adding a

term to the equation to account for the voltage drop across

the output resistance:

NoteWe can use the port 2 current in this equation because the equation for port 2

is an implicit equation. Recall that when the equation for port n is implicit, the

simulator appends the current through port n to the list of unknowns and, therefore,

the value of _in is available.

This model of an ideal amplifier as two-port SDD with the mixture of explicit and

implicit equations is shown below.

iiviRi¤ (). =

¥

i1Givi× =

fvi()VsAviVs¤ () tanh =

voVsAviVs¤ () tanhioRo+ =

### Page 122 from 216

5-22 SDD Examples

Custom Modeling with Symbolically-Defined Devices

Note the following points:

• There are several parameters whose values are set by the user then passed to

the device: G

i (input conductance), A (gain), Vs (saturated output voltage), and

R

o (output resistance).

•_v1, _v2, and _i2 are assigned to variables (vi, vo, and io, respectively), and the

variables are used in the SDD equations.

• The final form of the implicit equation for port 2 is written so that it equates to

zero.

The SDD is simulated in the design TestAmp.dsn. DC and harmonic balance

simulation results are shown in Figure 5-4.

• The first plot is a DC plot of v

o versus vi.

• The second plot is harmonic balance results showing output power and gain as

the amplifier saturates.

Figure 5-4. Simulation Results for the Ideal Saturating Amplifier

### Page 123 from 216

SDD Examples 5-23

Ideal Mixer

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

Tutorials/SDD_Examples_prj/networks/IdealMixer.dsn

The equivalent circuit for an ideal mixer is shown in Figure 5-5.

Figure 5-5. Equivalent Circuit for an Ideal Mixer

The ideal mixer is a three-port device, so three equations are required to define its

constitutive relationship. Based on the circuit above, the following three equations

can be used to represent the current at each port:

i

rf = vrf/Z

i

lo = vlo/Z

i

if = (vif*vrfvlo)/Z

These equations are voltage-controlled and can be implemented using explicit SDD

equations. The SDD is shown below.

### Page 124 from 216

5-24 SDD Examples

Custom Modeling with Symbolically-Defined Devices

In this setup _v1, _v2, and _v3 were used in the equations. Each port has a named

node, so the voltages will appear in the data display.

Results of a harmonic balance simulation of the mixer are shown in Figure 5-6.

Figure 5-6. Simulation Results for the Ideal Mixer

Figure 5-6 shows amplitude modulation effects in the time waveform of v

if. For this

simulation, v

rf is a sinusoid at 100 MHz with a DC offset and vlo is a sinusoid at 2

GHz.

### Page 125 from 216

SDD Examples 5-25

Nonlinear Capacitors

So far, all of the examples have dealt with nonlinear resistors. This section describes

nonlinear capacitors.

A nonlinear, voltage-controlled capacitor is defined in terms of its charge-voltage, or

q-v, relationship

For example, the q-v relationship for a linear two-terminal capacitor is

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

equation

To use the SDD to model a nonlinear voltage-controlled capacitor, note that given a

nonlinear charge Q(v), the current is

This is a voltage-controlled expression for the current. It differs from the constitutive

relationship of a voltage-controlled resistor because it contains a time derivative.

The time derivative is implemented in the SDD by specifying weighting function

number 1. Weighting function number 1 is predefined as jw which is the

frequency-domain version of the time derivative.

qQv() =

qCv=

iCv()

dv

dt ------- =

i

d

dt------Qv() =