# input resistance of differential amplifier

i have a question about the differential amplifier i know that the input resistance for the common mode is

Rin = rpi + 2 Beta Ree / 2 but my question is what is the input resistance for the differential signal ? this is the small signal equivalent circuit

• Input impedance (I'm not saying resistance as there are capacitors as well) is a small signal property so draw the small signal equivalent circuit and then start your analysis. – Bimpelrekkie Jun 16 '19 at 10:53
• this is the small signal equivalent ciruict that i used but i couldn't determine Rin – Gh-B Jun 16 '19 at 11:02
• Have a look at: metalab.uniten.edu.my/~jamaludin/… – Bimpelrekkie Jun 16 '19 at 13:41
• @Gh-B Please read Bimpelrekkie's link. Good information there, if you search through it. – jonk Jun 16 '19 at 18:36

I think, this question needs - at first - some definitions.

(1) Common mode is clearly defined: Vb1=Vb2

(2) Unsymmetrical diff. mode: Vb1 finite and Vb2=0.

(3) Symmetrical diff. mode: Vb2=-Vb1

(4) General symm. mode: Vb1 finite and Vb2 finite (with Vb1 not equal to Vb2).

Input resstances: For the first three cases, it is a realtively simple task to find the dynamic input resistances rin (here given at the base of Q1)

Case (1): rin=rpi+beta*2re (re: diff. resistance of the common emitter path) .

Case (2): rin=2rpi

Case (3): rin=rpi

Case (4): The input resistance at the base of Q1 depends on the signal Vb2 which is applied at the base of Q2. There is no textbook which gives an expression for the input resistance in this case (as far as I know). In this case, the input resistance must be calculated using superposition of the two cases (1) and (3). This is because each arbritrary combination of Vb1 and Vb2 can be split into the cases (1) and (3).

As the result, the formula for the input resistance will contain (and, thus, depend on) both input signals ! Therefore, no compact expression can be given.

• can u please explain a little more i'm not sure that i understand the four cases u talked about – Gh-B Jun 16 '19 at 10:54
• I don`t know what to furhter explain. The 4 cases are definitions for the 4 possible different combinatons of Vb1 and Vb2. – LvW Jun 16 '19 at 11:34
• Wants to know how to compute Rpi. – analogsystemsrf Jun 16 '19 at 12:19
• If case 2 (being one specific example of case 4) can be analyzed as a superposition of cases 1 and 3, why doesn't $\beta$ appear in the expression for $r_{\pi}$ there? – The Photon Jun 16 '19 at 14:28
• I do not understand the two last comments. I did not speak about the method how to find rpi. That is a complete other question. Of course, rpi depends on beta and the corresponding DC current Ic (rpi=beta*Vt/Ic). Something wrong in my answer? – LvW Jun 16 '19 at 15:05