Calculate Ic for an Ro out 33k

Thread Starter

psycoadam

Joined Oct 18, 2011
19
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
 

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t_n_k

Joined Mar 6, 2009
5,447
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.
 
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t_n_k

Joined Mar 6, 2009
5,447
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.
 

Thread Starter

psycoadam

Joined Oct 18, 2011
19
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
 

t_n_k

Joined Mar 6, 2009
5,447
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.
 

Thread Starter

psycoadam

Joined Oct 18, 2011
19
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?
 

t_n_k

Joined Mar 6, 2009
5,447
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.
 

Thread Starter

psycoadam

Joined Oct 18, 2011
19
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?
 

t_n_k

Joined Mar 6, 2009
5,447
Voc is the open circuit (i.e. infinite load resistance) output voltage and Isc is the output short circuit load current.
 

t_n_k

Joined Mar 6, 2009
5,447
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.
 
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