How can I find the input impedance of this CB stage? - Page 1
Forum section: electronics / beginners

author: giorgi3092
author_rank: Newbie
timestamp: July 31, 2021, 07:12:24 pm
content: Hello,I am given this problem:I draw small signal model like this:Then, I am not sure how to write the KCL at the emitter.A good samaritan online told me that the correct KCL would be:v_pi/r_pi + gm*v_pi + i_x = 0which yields R_in = v_x/i_x = r_e = V_T/I_C*alpha. which seems to be correct because I simulated in LTspice with typical values and calculations and simulation results match. Both gave 25 Ohm for I_c = 1mA, B=100 transistor.What I cannot understand at all is why we leave out the current that flows thru r_o??My naive KCL would be:v_pi/r_pi + gm*v_pi - gm*v_pi + i_x = 0 so, I would also write the current that flows out of the node thru r_o, simplifying to v_pi/r_pi + i_x = 0, which gives R_in = v_x/i_x = r_pi which is totally WRONG!Can anyone explain the weeds of this circuit? and why we leave r_o out of the KCL equation?

author: magic
author_rank: Super Contributor
timestamp: July 31, 2021, 08:40:34 pm
content: Well, I'm not very fluent in those models but input impedance of such stage is definitely the intrinsic emitter resistance (1/gm) of the transistor at given current (VT/Ie). Add to that any parasitic emitter resistance, plus base spreading resistance divided by β.

author: TimFox
author_rank: Super Contributor
timestamp: July 31, 2021, 08:51:27 pm
content: Similarly, the approximate basic input impedance at the cathode of a grounded-grid stage is 1/gm, since that is the small-signal ratio of a change in cathode current to a change in cathode voltage. If there is a cathode or emitter bias resistor in the circuit, then that is in parallel with the intrinsic input impedance.For the grounded-grid case, technically the small-signal input impedance isZin= (Rp+Zload) / (µ + 1). If the plate resistanceRp>>Zload, the load resistance, and µ >> 1, this reduces toZin=Rp/ µ = 1/gm. The proof for a BJT is left to the reader.

author: giorgi3092
author_rank: Newbie
timestamp: July 31, 2021, 09:18:49 pm
content: I don't think the replies address my question but thank you. In other words, yes you are right, the input impedance of the CB stage is approx 1/gm, but I am interested in how the KCL is written at the emitter in the above model, to arrive at the input impedance.

author: magic
author_rank: Super Contributor
timestamp: July 31, 2021, 09:39:06 pm
content: On second thought, maybe you aren't wrong. We are considering a somewhat atypical case here with no external collector load resistance of any sort - collector current is held absolutely constant. So obviously it cannot change with emitter voltage, only the base current changes due to Early effect. This is modeled by all current generated by gm subsequently being sunk by rodue to output swing while rπis the only input impedance term that remains.Of course it's a very narrow region of operation. Push the transistor into breakdown or saturation and it all falls apart. I think SPICE should be able to model it and produce result much higher than 1/gm.Quote from: giorgi3092 on July 31, 2021, 07:12:24 pmeditA related problem occurs when trying to make a very high impedance current sink by cascoding. Voltage change at the cascode collector induces some small change in Vbe and Ib and the change in Ib is simply subtracted from Ic, even if the lower device has enough impedance to keep Ie constant against Vbe.