Small signal analysis of common collector circuit

Thread Starter

uhf737

Joined Dec 9, 2017
14
Hello.
I am having a bit of a Problem solving this task. I need to calculate Rin, Rout and the current gain Ai ("e" is in and "a" is out)

kesb.png

This is how I tried to solve it :

1)

Re = ReT = Ue/ie for Ua=0

Ue = ie*rbe+Re*(ie+ie*ß) solved for Ue/ie : Re = rbe + (1+ß)Re

2)

Ra = Ua/ia for Ue = 0

Ua = Re*(ube/rbe+ube/rbe*ß - Ua/rce+ia) for ube = -Ua/rbe

Ua = Re*(-Ua/rbe - Ua/rbe*ß - Ua/rce +ia) solved for Ua/ia = Re/(1+(1+ß)*Re/rbe+Re/rce)

3)

Ai = ia/ie for Ua=0

ie = ib
ia = Ua/Re - ib - ib*ß

ia/ie = -ib - ib*ß/ib = - ib*ß

I think 3) is obviously wrong since the current shouldnt be inverted...
 
Last edited:

Thread Starter

uhf737

Joined Dec 9, 2017
14
I'm kind of lost here, what do you mean by bias conditions ? be has to be positive voltage while cb has to be negative voltage ?
 

Thread Starter

uhf737

Joined Dec 9, 2017
14
The input/output resistance seems to be correct judging by the solution I have but the current gain is definitely off.

EDIT: Maybe there is something wrong with the way I am going at it. 1. Step : disconnect all DC sources, Step 2 : rewrite the circuit in a way that simplifies further calculations

Next is the Input Impedance which is the input voltage divided by the current ie that I feed into the transistor (Vout is zero for this calculcation)

Output Impedance is the output voltage divided the current I feed into the exit of the transistor (Vin is zero for this calculation)

Voltage gain is simply Vout/Vin which is about 1 for this circuit

Current gain is output current/input current (output voltage is zero for this calculation)
 
Last edited:

Jony130

Joined Feb 17, 2009
4,969
Look at this exampel

Zin = Vin/Iin


So, from the KVL ( II Kirchhoff's law ) we will have:

Vin = Ib*rbe + Ie*Re||rce

Additional we knows

Ie = Ib + Ic = Ib + β*Ic = (β + 1)*Ib

Vin = Ib*rbe + Ie*Re||rce = Ib*rbe + (β + 1)*Ib*(Re||rce) = Ib*( rbe + (β + 1)*(Re||rce) )

Zin = Vin/Iin = rbe + (β + 1)*(Re||rce)

where || means parallel connected.

Also to avoid confusion in transistor circuit's you shoud never used Ue and Ie as input variables.
Because the most of us will treat "Us" as emitter voltage and "Ie" as emitter current. This is why I used Vin and Iin instead.
 
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