Input impedance of BJT amplifier


by likephysics
Tags: amplifier, impedance, input
likephysics
likephysics is offline
#1
Jan21-12, 01:11 PM
P: 596
1. The problem statement, all variables and given/known data
Find input resistance of the ckt (see attached)


2. Relevant equations



3. The attempt at a solution
Q2 is diode connected, so I replaced Q2 with VBE resistance (rbe or r∏).
So, Rin is rbe1+(β+1)rbe2

But the answer is somewhat different, it's rbe1+ (β+1) (rbe2||1/gm2)
Where did 1/gm2 come from?
Attached Thumbnails
cascode.png  
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vk6kro
vk6kro is offline
#2
Jan21-12, 06:26 PM
Sci Advisor
P: 4,003
Q2 is also a transistor and it draws collector current as well as base current.

So, this affects the total resistance of Q2 in this circuit.
likephysics
likephysics is offline
#3
Jan22-12, 09:19 AM
P: 596
I tried to draw an equivalent diagram and solve. see attachment.
Basically, rbe and gm*vbe are both shorted (because of collector base short of Q2).

I attached a test source Vx to determine the input impedance of just Q2. So impedance will be Vx/ix.
After solving, I got 1/gm (assuming β>>1).

From the equivalent ckt,
Vx=Vbe
ix = Vbe/rbe +gmVbe

ix=Vbe (1/rbe+gm)

ix = Vx (1/rbe+gm)

Rin = Vx/ix = 1/(1/rbe+gm)

rbe = β/gm

Rin = 1/(gm/β +gm)
Rin = 1/gm((1+β)/β))

if β>>1, then (1+β)/β = 1

Rin = 1/gm
Attached Thumbnails
cascode2.png  


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