Small-signal transfer function from this differential input

Click For Summary

Discussion Overview

The discussion revolves around deriving the small-signal transfer function from a differential input in the context of a BJT circuit. Participants explore various approaches to solving the problem, including the use of small signal equivalent circuits and specific equations related to BJTs.

Discussion Character

  • Homework-related
  • Technical explanation
  • Debate/contested

Main Points Raised

  • Some participants suggest using small signal equivalent circuits and Kirchhoff Current Law, while others argue against this approach, stating that the necessary equations are sufficient without equivalent circuits.
  • A participant proposes using the approximation ex ≅ 1 + x for small values of x as a potential method to simplify calculations.
  • There is a challenge regarding the derivation of the answer 1/2*gm using only gm, with one participant expressing confusion about the relevance of the exponential function in this context.
  • Another participant provides a formula for gm in terms of the differential currents and voltages, indicating a specific approach to the problem.
  • Participants express differing opinions on the best method to approach the problem, with some favoring direct use of gm and others suggesting alternative formulations.

Areas of Agreement / Disagreement

Participants do not appear to reach a consensus on the best approach to derive the small-signal transfer function, with multiple competing views on the use of equivalent circuits and the application of specific equations.

Contextual Notes

There are limitations regarding the assumptions made about the circuit parameters and the definitions of variables, which may affect the derivation process. Some mathematical steps remain unresolved, particularly in relation to the use of exponential functions and their implications in the context of the problem.

CorHawk
Messages
2
Reaction score
0

Homework Statement


q1.png

2. Homework Equations [/B]
Small Signal Equivalent Circuit, Kirchhoff Current Law, and BJT equations mentioned in the question.

The Attempt at a Solution


q1a_1.png

It looks like I did something wrong. Can someone help me with fixing this?
 
Physics news on Phys.org
CorHawk said:

Homework Statement


View attachment 81419
2. Homework Equations [/B]
Small Signal Equivalent Circuit, Kirchhoff Current Law, and BJT equations mentioned in the question.

The Attempt at a Solution


View attachment 81420
It looks like I did something wrong. Can someone help me with fixing this?
I would not use equivalent circuits for this. You're given all the equations you need to solve the problem without resorting to equiv. ckts.
Hint: at some point use ex ≅ 1 + x for 0 ≤ x << 1.
OR you can do it with just gm.
 
Last edited:
rude man said:
I would not use equivalent circuits for this. You're given all the equations you need to solve the problem without resorting to equiv. ckts.
Hint: at some point use ex ≅ 1 + x for 0 ≤ x << 1.
OR you can do it with just gm.

I don't understand how you want to get to the answer 1/2*gm by only using gm and nothing else. And I don't see how e^0=1 would be related to this.
 
Last edited:
CorHawk said:
I don't understand how you want to get to the answer 1/2*gm by only using gm.
I'll get you started:
gm = dI1/d(Vb1 - Ve) = -dI2/dVe
where Vb2 = 0 is assumed wlog ("without loss of generality"). Vb is base voltage, Ve is emitter voltage.
And I don't see how e^0=1 would be related to this.
That would come in handy if you choose to use I = Isexp(qVbe/kT) instead of gm directly.
I recommend using gm directly, it's shorter.
 
Last edited:

Similar threads

Engineering Small Signal Input Resistance of a BJT amplifier
  • · Replies 23 ·
Replies
23
Views
5K
From differential equations to transfer functions
  • · Replies 5 ·
Replies
5
Views
3K
Transfer Function of a FET Differential Amplifier
  • · Replies 4 ·
Replies
4
Views
3K
Engineering What is wrong in this 2nd order transfer function?
  • · Replies 2 ·
Replies
2
Views
2K
Engineering Diff gain of a push pull degenerated differential pair
  • · Replies 6 ·
Replies
6
Views
3K
Engineering Is it possible for a low pass filter to have such a transfer function?
  • · Replies 16 ·
Replies
16
Views
2K
Does the transfer function exist for an unforced system?
  • · Replies 12 ·
Replies
12
Views
4K
Transfer function with multiple inputs
  • · Replies 3 ·
Replies
3
Views
7K
Engineering Determine the input impedances of a circuit
  • · Replies 12 ·
Replies
12
Views
3K
Finding the transfer function for a difference amplifier
  • · Replies 8 ·
Replies
8
Views
2K