7
‘Real Time’ Large Signal
Modelling
7.1 Introduction
Modern large signal modelling packages offer extremely accurate results if good
models are provided. However, they are often slow when optimisation is required.
It would therefore be very useful to be able to optimise the performance of a
circuit, such as the load network for a power amplifier, by being able to vary the
important parameter values as well as the frequency and then to observe the
waveforms on an ‘oscilloscope-like’ display in real time.
This chapter describes a circuit simulator which uses the mouse with crosshatch
and slider controls to vary the component values and frequency at the same time as
solving the relevant differential equations. The techniques for entering the
differential equations for the circuit are described. These differential equations are
computed in difference form and are calculated sequentially and repetitively while
the component values and frequency are varied. This is similar to most commercial
time domain simulators, but it is shown here that it is relatively easy to write down
the equations for fairly simple circuits. This also provides insight into the operation
of large signal simulators. The simulator was originally written in QuickBasic for
an Apple Macintosh computer as this included full mouse functionality. The
version presented here uses Visual Basic Version 6 for a PC and enables the data to
be presented in an easily readable format. A version of this program is used here to
examine the response of a broadband highly efficient amplifier load network
operating around 1-2GHz.
Fundamentals of RF Circuit Design with Low Noise Oscillators. Jeremy Everard
Copyright © 2001 John Wiley & Sons Ltd
ISBNs: 0-471-49793-2 (Hardback); 0-470-84175-3 (Electronic)
Real Time Large signal modelling 275
7.2 Simulator
A typical simulator layout is shown in Figure 7.1. It consists of a main ‘form’
entitled Form 1 which displays four waveforms, and in this case, always shows

I3
Figure 7.2
Broadband amplifier used for simulation
For ease the circuit is driven by an ideal switch. For rapid analysis, we shall also
make approximations about the transient response of the switch on closure. This
reduces the transient requirements and hence stability of the software without
introducing significant errors. In fact this is a potential advantage of this type of
modelling as one can occasionally and deliberately disobey certain fundamental
circuit laws for short periods of time without significantly affecting the waveform.
The final result can then be checked on a commercial simulator or on this
simulator by modelling the components more accurately.
Using the circuit shown in Figure 7.2 the following steps should be performed.
1.

Write down the differential and integral equations for the circuit.
2.

Convert these equations to difference equations so they can be solved
iteratively.
3.

Use the mouse and slider controls to control the variation of selected
components and frequency.
4.

Plot the required waveforms while showing the values of the varied
components.
Real Time Large signal modelling 277
This will be illustrated for the example shown in figure 7.2. The differential
equation for the series arm consisting of

−−=
RI
C
Q
V
Ldt
dI
1
2
1
0
1
1
1
(7.2)
This is now written in ‘difference form’ by relating the new value to the previous
value. For example:
() ( )








−−=
∆
−
−

C
Q
V
L
t
II
nn
1
2
1
0
1
111
(7.4)
Note that in a computer program the (
n
-1) term can be given the same variable
name as the (n) term as the new value assigned to the variable is now equal to the
old value plus any changes. In this example the equation written in the program
would therefore be:






−−+=
RI
C
Q

(7.6)
278 Fundamentals of RF Circuit Design
1
2
0
C
I
dt
dV
=
(7.7)
In difference form:
() ( )
1
2
100
C
I
t
VV
nn
=
∆
−
−
(7.8)
As before the form of the equation used in the computer program would be:
()
1
2

() ( )
2
0
144
L
VV
t
II
S
nn
−
=
∆
−
−
(7.12)
The equation as it would appear in the computer program is therefore:
()
2
0
44
L
VVSt
II
−
+=
(7.13)
The charge equation for
C
2