Common-Collector Circuit Small Signal Analysis (BJT)

first thing to check for a circuit with a transistor

check that the transistor satisfies active mode conditions

(1) T-model for npn transistor in AC analysis

• best for common base to find voltage gain, input resistance seen by source, output resistance seen by load

(2) T-model for npn transistor in AC analysis

• best for common base to find voltage gain, input resistance seen by source, output resistance seen by load

(10) hybrid pi model for npn transistor

hybrid pi model for npn transistor

use for common emitter/collector and sometimes common base if it’s more comfortable

difference between the hybrid / t models for npn transistor vs pnp transistor

they’re the same but you have to switch the polarity of the voltages and the directions of the currents

how to tell if a circuit is common-base, common-emitter, or common-collector

(this rule doesn’t apply in all cases) → for instance, if the AC ground is directly connected to emitter, then it’s common-emitter

you cannot express any of these small signal parameters with a varying small signal current or voltage

BUT you can express them with signal variables AS LONG AS they can be cancelled out in the final expression

what is Rin

the input resistance, parallel to v_i → it’s the resistance that the input signal source “sees’ looking into the transistor input terminal (where vin is measured) with independent sources turned off

what is Rout

the output resistance → the resistance seen by the load looking into the output terminal of the transistor (/amplifier), in parallel with v_o

which is being amplified by the transistor? (DC values or AC values)

AC values. DC values are always constant

typical values for the gains in a common-collector circuit

current gain: SLAYYYYYYYYYYYYYY

voltage gain: such an L

how to find Rin

solve for v_in/_in (v_in and i_in both have their own expression that you must find)

how to “reflect” a resistor

the resister for i_e wouldve been R_L, since , but since we’re getting all the resistances for i_b, it’s (1 + beta)R_L

• R_L is in the direct branch of i_e, not i_b, but we can relate i_e and i_b together with i_b = i_e/(1 + beta)

• so therefore i_e/R_L → i_b/(1 + beta)R_L

when you’re trying to find Rout, you must:

cut off everything that comes “before” it

here, R_L is cut off

how to find Rin and Rout

use V_T/I_T

rbmr: things are in PARALLEL, not series, if they ….

share two nodes, and usually one is the ground node BUT watch out for if there’s an open circuit in the branch

process of analysis for amplifier

almost always try to simplify by….

noticing which resistances are parallel and combining them

when doing a KVL loop, avoid :

current sources

relationship between i_e and i_c

i_c = i_e * alpha

always look for equivalent resistance Rin and Rout in»>

small-signal domain, so deactivate all DC sources and short circuit all capacitors

in what situation can you turn off a dependent source in thevenin resistance calculation

if you can prove the dependent source to be equal to 0

• in the example in the image, i_e must be shown as 0

how to tell that you need to take early effect into account

when the question says “V_A < infinity” or gives a numerical value for V_A; if it says “V_A = infinity” ignore early effect

what to do if a problem involves early effect

change the equivalent T or hybrid-pi model to include r_o (see images → generally, r_o is in parallel with the dependent current source)

what do you notice here

r, is parallel with R_L

_{so you can combine them DUMMYYY}

the input resistance looking RIGHT into the base is _____ times the TOTAL resistance in the emitter

(beta + 1)

***input resistance looking right into the base is equal to v_i/i_b

you can rearrange the relation Rin = vi/ii to be

ii = vi/Rin

neat trick to find i_o/i_i

it generally equals to (v_o/v_i)*(R_in/R_L)

how to simplify circuits so they’re easier to compute