Understanding the Role of Ro in Amplifier Design

[null void]

Homework Statement

i) I am to find I_B, I_C and r_e
ii) Determine Z_in and Z_out

The Attempt at a Solution

To find I_B,

i)

I use the KVL, start from base

V₂ = I_B R₁ + V_BE ,
I assume my V_BE = 0.7 V
I_B = 23.8462 μA

then my I_C = I_B H_FE
I_C = 2.3846 mA

For r_e = 26m V / I_C
r_e = 10.9 Ω


ii)

Z_in = R_B // H_ie
Hie = H_fe r_e = 1090 Ω
Z_in = 1.087 kΩ

Z_out = R_C...I think this is where i need to use r_o, but i have no idea wat is it referring to...

 

[The Electrician]

I think Ro is 1/hoe.

 

[null void]

If it is 1/H_oe, then the Z_out

Z_o = r_o // R_C
Z_o = 4.012 kΩ

then i will proceed to the next part,
iii) calculate A_v and A_i

I_b = Vin / H_ie
V_out = -h_fe I_b (r_o // R_C)
= -h_fe ( Vin / H_ie ) (r_o // R_C)

A_v = V_out / V_in
=- h_fe / h_ie (r_o // R_C)
= -368.114 ...Awkward number...

for A_i,

I_in = V_in / 390k + V_in 1090
= V_in (1/390K + 1/1090)

I_out = I_RC ...this is correct right?
= -h_fe I_b (r_o//R_c)/R_c

A_i =( -h_fe/ h_ie)(r_o//R_c)/R_c
= -93.053

Is all these working step correct?

 

[The Electrician]

You have used a factor hfe in some places where strictly the proper factor should be (hfe+1). For example you have:

Hie = Hfe re

but it should actually be Hie = (Hfe+1) re

Other than this, which leads to a very small error in some calculations (an error which is negligible if hfe is large), your answers are correct.

 

[rude man]

Check your r_e. Do you have the correct formula?

Not sure if Zo is meant to include C1 or not. Same for Zin and C2, come to think of it.

EDIT: actually, this circuit is saturated: the collector current computes to 100*(9.3V/390K) = 2.3846 mA which x 4.3K = 10.25V which exceeds the collector supply.

 

[null void]

EDIT: actually, this circuit is saturated: the collector current computes to 100*(9.3V/390K) = 2.3846 mA which x 4.3K = 10.25V which exceeds the collector supply.

yeah i, but it still asking for amplification...

and about the re, do u mean the Ebers–Moll equation? Well, i still don't know how to use it yet, so i wil syick with the 26mv/ic approximation first.

 

[rude man]

yeah i, but it still asking for amplification...

Amplification is zero.

You might have the right formula for re after all, I don't know your model.

 

[The Electrician]

rude man, were you referring to the fact that the usual formula for r_e is r_e = 26m V / I_E rather than r_e = 26mV / I_C?

Of course, if hfe is large, the difference is usually negligible, and somewhat variable since different people choose different values for the thermal voltage; sometimes 26 mV, sometimes 25 mV, etc.

 

[The Electrician]

null void, tell your instructor that you noticed that the transistor is saturated, so you assumed that V1 is actually 12 volts!

Or to really impress the instructor, tell him you analyzed a slight variation in the circuit, namely that V2 is gone and R1 is connected from collector to base.

 

[rude man]

rude man, were you referring to the fact that the usual formula for r_e is r_e = 26m V / I_E rather than r_e = 26mV / I_C?

Of course, if hfe is large, the difference is usually negligible, and somewhat variable since different people choose different values for the thermal voltage; sometimes 26 mV, sometimes 25 mV, etc.

No, I had in mind re = 26mV/ib but that was probably wrong. As I said, i didn't know the OP's model.

EDIT: 26 mV/ib is the input impedance to a decently-biased BJT (Vce between say 1V and 20V):

Ic = Is exp(Vbe/Vt)
∂Ic/∂Vbe = Is (1/Vt) exp(Vbe/Vt) = Ic/Vt
1/Zin = ∂Ib/∂Vbe by definition = (1/β) ∂Ic/∂Vbe = (1/β)(Ic/Vt)
Zin = Vt/(Ic/β) = Vt/Ib = 26mV/Ib

 

[rude man]

Or to really impress the instructor, tell him you analyzed a slight variation in the circuit, namely that V2 is gone and R1 is connected from collector to base.

That would actually be a viable circuit! (the one with 12V Vcc is too dependent on beta).

 

[null void]

If i add a resistor at the emitter to the circuit and change the V1 and V2, is it possible that for the Vce to become negative value, is this also a case of saturation?

 

[NascentOxygen]

If i add a resistor at the emitter to the circuit and change the V1 and V2, is it possible that for the Vce to become negative value, is this also a case of saturation?

A negative value for VCE would mean the circuit bears no resemblance to an amplifier.

An emitter resistor would allow a more stable design, but choose a lower value for V2.