Rik Min - Transistor

5.5 The computer simulation program TRANSISTOR with a model about an active electronical circuit.

See also my e-book on internet: chapter 5 and figure 5.11.

Many mathematical models of a transistor are known. Some of these models are matrix-models, treating the transistor as a black box, presenting sets of values of output variables as a result of sets of values of input parameters like input impedance, voltage gain etc. Other models simulate the transistor in a more transparent way. In these models, the transistor is described by means of an electronic circuit. The models can be used in order to study the transistor's behaviour in a dynamic way by changing the parameters.

The model of a transistor, implemented in the prototype TRANSISTOR, belongs to the second type of models. It describes the behaviour of a transistor in a normal low signal amplifier circuit. The model has been developed for educational applications by Min and Malhotra (1988) and Min and Van Leeuwen (1990, not published).

Educational value

Simulations of electronic networks may be useful in the physics or electronics curriculum as a training before starting real experiments. The consultation of content specialists, curriculum specialists and specialists in didactics would be required in order to obtain the information needed for the improvement of the prototype in order to make it suitable for use in a didactic environment.

Nevertheless, prototypes similar to TRANSISTOR may prove very useful in everyday physics teaching to replace expensive or difficult experiments.

Model description

TRANSISTOR has been first implemented in MacTHESlS by Malhotra in 1988. The purpose of the implementation was to test the performance of the design system with respect to the implementation of models originating from the subject of Physics. Min and Van Leeuwen have implemented TRANSISTOR in MacTHESlS in 1990; later sometimes in JavaTHESIS; see figure 3 and 4. The default values of the parameters and the starting values of his model are:

A =  0.01               <- V 
f =  100.0              <- Hz 
ui   =  0.0             <- V 
beta =  200.0   
IC0 =  1.0              <- mA 
q =  1.6E-19            <- Asec
K =  1.38E-23           <- J/K
T =  100.0              <- K
S =  40.0*IC0           <- (q / K.T).IC0 = 40.0 
rb =  beta/S            <- 5 kOhm 

Ucc =  12.0                       <- V 
IB0 =  IC0/beta                   <- 1/200=0.005 mA 
IE0 =  (beta + 1)*IB0             <- (200+1)0.05 = 1.005 mA 
RC =  4.0                         <- kOhm
R2 =  56.0                        <- kOhm
RE =  (0.5*Ucc - IC0*RC)/IE0      <- 2/1.005 kOhm
Ir =  (0.7 + RE*IE0)/R2           <- 2.71/56 = 0.04839 mA 
R1  =  (Ucc-0.7-RE*IE0)/(IB0+Ir)  <- 174.0 kOhm 

ib  =  ui*S/beta    
uo =  -beta*ib*RC

Figure 1. The model of the computer simulation program TRANSISTOR with the input and output.

Figure 2. The model of the computer simulation program TRANSISTOR with the DC and the AC component.

The most essential parts of the first version of the model (here written in Pascal) are:

Repeat
  t := t + dt;
  ui := A * sin (2 * 3.1418 * f * t); 
  S := 40 * IC0;    
  IB0 := IC0 / beta;
  IE0 := (beta+1) * IB0;
  RE := (0.5*Ucc - IC0*RC) / IE0;
  Ir := (0.7 + RE*IE0)/R2;
  R1 := (Ucc - 0.7 - RE*IE0) / (IB0 + Ir);
  i1:=ui/R1;
  i2:=ui/R2;
  ib := ui * S / beta;
  ii := i1+i2+ib;
  uo := -beta*ib*RC;
  io :=uo/RC;
Until t > Tmax;

The most essential parts of the last version of the model (here written in Java) are:

for (....)
{
  t := t + dt;

  ui := A * Math.sin (2 * 3.1418 * f * t); 
  if (ui>0.01) ui = + 0.01;
  if (ui<0.01) ui = - 0.01;

  UB = Ucc*R2/(R1+R2);
  URE = URE + ((UB - 0.7) - URE)*0.03;
  IE0 = URE/RE; 
  IC0 = IE0;
  UC = Ucc - IC0*RC; 

  ui1 = ui1 + (ui - ui1)*0.2;
  uo = -40*IC0*RC*ui1;

  U0 = UC + uo;
};

The prototype TRANSISTOR is first designed according to the description of the student's environment of MacTHESlS. In this application three windows are present. In the other versions mostly two window are visualized. The circuit consists a 'standard' transistor, some resistors and a function generator. See the online example:

Online example 1. the microworld of TRANSISTOR (version Adapt-project, 2004)

Figure 3. Output of the computer simulation program TRANSISTOR, version 2000

Students can change the form of the input (sinus, block or pulse), the frequency and the amplitude of the input on the circuit on in other regions by clicking on the function generator or something. Furthermore, the properties of the electronic network can be changed by clicking sometimes in one of the resistors or some part of the transistor.

Figure 4. Output of the computer simulation program TRANSISTOR, version 2002

Enschede, 1996 - 2002