I am asked to find an Ic value to make the output impedance value equal to 33kohms.

I have attached the circuit and the parameters given are:
Parameters: BF = 100, VBE = 0.7 V, VA = 88 V, VT = 25.8 mV.

Calculate IC to make the output impedance equal to 33 kOhm

After making a small signal model of the circuit it seems to me that

gm = Ic/Vt; r(pi) = VT/Ib; and then that means ro = ABS(VA)/Ic...

I feel I am doing something wrong here because if the answer is really that easy I have spent way too much time on this problem. Some acknowledgment that I did it right or at least a push in the right direction would be wonderful.

Also I know the second transistor is acting like a diode but I am not quite sure how it would effect the current which in turn would effect the output impedance.

Please Help

 

A reasonable approximation for Ro is VA/IC, provided VA>>VCE. So in the absence of any other qualifying information I'd say you are probably on the right track. I'd probably also want to think a bit more about the presence of Q2 and its effect. Particularly as Q2 is a 'non-linear' emitter load.

 

I am confused as to what you mean by "non-linear"

 

Non-llinear? Well to the extent that the effective Q1 AC emitter load presented by Q2 is dependent on the quiescent current flow in Q1 & Q2. Sure, it can be linearized as a small signal equivalent, but one has to know the quiescent current first or at least have the means of solving for the unknown quiescent current - which is the essence of this problem. I imagine the value of the amplifier Ro probably does depend on [Q2] effective small signal resistance. After all it will effect the overall amplifier gain.

 

Thank you for your input. Now that I somewhat understand what I am looking for I am having trouble solving for the Q-point. From what I read in my text books I am either not given enough information or I am getting my Ib = 0, which makes my Ic = 0. Maybe just a little more explanation would be helpful. Thanks Again

 

It's hard to comment about a solution because it's such a 'minimalist' problem. I would think for instance that the source resistance has a significant impact on the amplifier output resistance but there's no mention of source resistance.

Presumably what you show in post #1 is all the information you were given.

 

Yes, that is all the information I was given... which is why I am having such a difficult time with this problem.

 

OK - have you drawn up the Hybrid-PI equivalent circuit?

 

Yes, I did, my only concern with my Pi model is the second npn that acts like a diode is connected to the emitter of Q1, so does that mean the base of Q2 is connected to the emitter?

 

I have attached what I think the small signal model would look like. So i am assuming that looking into Q2 the resistance would be R(pi)||ro?

 

With respect to Q2 - treat it as a a diode with a dynamic resistance re of (VT/IE1) Ω which sits in the emitter leg of Q1. IE1 is the static emitter current for Q1. In fact the value rπ=β*re since both Q1 and Q2 have the same emitter currents.

Obviously you don't know the value of IE1 [=Ic1+Ib1]=(1+β)*Ib1

The trick is obviously to derive a relationship for Rout (not Ro=VA/Ic) based on the unknown value of Ic. Alternatively, you use a trial & error method in which you make an initial guess for a value of Ic and check what Rout results - then adjust your guess to achieve a better result nearer 33kΩ. Try starting with a collector current of 5mA. A least you'll see what's going on in the equivalent circuit with respect to the various values.
Remember Rout=Voc/Isc.

 

Ok, I understand the diode and replaced my emitter load. I understand the relationship
IE1 = [Ic1+Ib1]=(1+β)*Ib1

so then Voc is the output voltage on the collector and Isc is the collector current?

 

Voc is the open circuit (i.e. infinite load resistance) output voltage and Isc is the output short circuit load current.

 

FYI:

For a large β value a reasonable approximate relationship for the output resistance is

Rout≈2VA/Ic

which is a rather simple outcome. [I can post a 'proof' if there is any ongoing interest.]

This relationship provides a good starting point for deciding on a value of Ic to give you the required Rout.

You'll probably find Rout is quite sensitive to small changes in Ic.

A value of Ic=5.3mA seems about right.