# Audio Amplifier Analysis

## Main Question or Discussion Point

Hi. I'm trying to analyse an audio amplifier circuit (DC, frequency response, stability, etc.).

I began with the DC bias analysis but I'm having troubles finding where to start. I've attached the full circuit and a DC simplified version. I've placed an 8 ohm resistor as the load (8 ohm speaker), is this correct?

All I could come up with is (I'm assuming collector currents equal emitter currents):
##I_{C1}=V_{EB4} /R_6##
##I_{C2}=I_1-I_{C1}##
##V_{B4}=V_{CC}-V_{EB4}##

Should I start by doing the two-port equivalent of the feedback network (C3, R4, R5)? Somewhere else... ?
I'm pretty much lost.

PS: I also found that ##I_{R17}=V_{BE9}/R_{17}## but that got me nowhere.

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Without going into nonlinear equations and numerical/iterative solution we are force to use to use a simplified solution based on some assumption.
Because this circuit is nothing more then a opamp based/style non-inverting amplifier with the gain of one (for DC voltage this circuit work just like voltage follower, but AC closed loop gain is Av ≈ 1+ R5/R4 ≈ 22V/V ).
So Vin = 0V this means that also is equal 0V ( we ignore Q1 and Q2 the base current).

Ic1 ≈ Ic2 ≈ I1/2 ≈ 1.18mA
Ic4 ≈ (Vcc - VbeQ6)/( R9 + R10) ≈ 5.2mA
Ic9 ≈ Ic4 - VbeQ9/R17 = 5.2mA - 0.38mA ≈ 4.82mA

The output stage current is undetermined because we do not know the exact value for a Vbe5 and Q6.

The simulation show as this result
Ic1 = 0.856mA
Ic2 = 1.51mA
Ic4 = 5.25mA
Ic9 = 4.81mA
Ic5 = 4.65mA
Ic6 = 3.8mA
Ic7 = 208mA
Ic8 = 209mA

First of all, thanks for replying!

The simulation show as this result
Ic1 = 0.856mA
Ic2 = 1.51mA
Ic4 = 5.25mA
Ic9 = 4.81mA
Ic5 = 4.65mA
Ic6 = 3.8mA
Ic7 = 208mA
Ic8 = 209mA
I've attached the results of the simulation that I ran.

Ic1 ≈ Ic2 ≈ I1/2 ≈ 1.18mA
For the differential amplifier I found the following (which more or less matches the simulation):
##I_{C1}=V_{EB4} /R_6=0.47 V/560 Ω=839.29 μA##
##I_{C2}=I_1-I_{C1}=1.54 mA##
##V_{B4}=V_{CC}-V_{EB4}=35 V-0.47 V=34.53 V##
##V_{B1}=-I_{C1}/β_{1}.(R_2+R_3)-V_{BE1}=-839.29 μA/325 . (22 kΩ+1 kΩ)-0.66 V=-0.72 V##
##V_{CE1}=V_{B4}-V_{B1}=34.53 V+0.72 V=35.25 V##
##V_{CE2}=V_{CC}-V_{B1}=35 V+0.72 V=35.72 V##

Ic9 ≈ Ic4 - VbeQ9/R17 = 5.2mA - 0.38mA ≈ 4.82mA
I understood this perfectly.

Ic4 ≈ (Vcc - VbeQ6)/( R9 + R10) ≈ 5.2mA
However I don't understand this equation. I get that ##I_{C4}=I_{R9}=I_{R10}## but I'm not seeing how the voltage drop across R10+R9 equals Vcc-Vbe6.

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On the speaker front:

Speakers have frequency dependent impedances. They vary between about ½ the nominal (8Ω) to perhaps 5 times the nominal depending on the box they are in. (The box affects the power transfer depending on frequency.)

meBigGuy
Gold Member
but I'm not seeing how the voltage drop across R10+R9 equals Vcc-Vbe6.
Actually, it equals Vcc - Vr14 -Vbe6

If you assume the output voltage is 0V, then the voltage at the top of R9 is Vbe6+Vr14 below 0. But if you assume Ir14 == 0 then that means Vbe6 could be very low or zero.

On the other hand, If it is operating class A, then there is a drop across R14 even if Vrl == 0.

I've attached the results of the simulation that I ran.
For the differential amplifier I found the following (which more or less matches the simulation):
##I_{C1}=V_{EB4} /R_6=0.47 V/560 Ω=839.29 μA##
##I_{C2}=I_1-I_{C1}=1.54 mA##
##V_{B4}=V_{CC}-V_{EB4}=35 V-0.47 V=34.53 V##
##V_{B1}=-I_{C1}/β_{1}.(R_2+R_3)-V_{BE1}=-839.29 μA/325 . (22 kΩ+1 kΩ)-0.66 V=-0.72 V##
##V_{CE1}=V_{B4}-V_{B1}=34.53 V+0.72 V=35.25 V##
##V_{CE2}=V_{CC}-V_{B1}=35 V+0.72 V=35.72 V##
Are you sure about VB1 ?? Notice that Q1 is a NPN transistor so the base current will flow into the Q1 base and this is why VB1 = Ib1*(R2 + R3) ≈ 60mV and VE1 = VB1 - Vbe1. Also to be more precise Ic1 is equal to Vbe4/R6 + IB4

However I don't understand this equation. I get that ##I_{C4}=I_{R9}=I_{R10}## but I'm not seeing how the voltage drop across R10+R9 equals Vcc-Vbe6.
Notice that the voltage at Q6 emitter is equal to 0V (as we assumed) and if we ignore R14 voltage drop the voltage at Q6 base is Vbe6 below the 0V. So this means the voltage across r9 and R10 is Vcc - Vbe6.

On the speaker front:

Speakers have frequency dependent impedances. They vary between about ½ the nominal (8Ω) to perhaps 5 times the nominal depending on the box they are in. (The box affects the power transfer depending on frequency.)
Thanks, will look into that.

Actually, it equals Vcc - Vr14 -Vbe6

If you assume the output voltage is 0V, then the voltage at the top of R9 is Vbe6+Vr14 below 0. But if you assume Ir14 == 0 then that means Vbe6 could be very low or zero.

On the other hand, If it is operating class A, then there is a drop across R14 even if Vrl == 0.
Notice that the voltage at Q6 emitter is equal to 0V (as we assumed) and if we ignore R14 voltage drop the voltage at Q6 base is Vbe6 below the 0V. So this means the voltage across r9 and R10 is Vcc - Vbe6.
Now I got it, thanks!

Are you sure about VB1 ?? Notice that Q1 is a NPN transistor so the base current will flow into the Q1 base and this is why VB1 = Ib1*(R2 + R3) ≈ 60mV and VE1 = VB1 - Vbe1. Also to be more precise Ic1 is equal to Vbe4/R6 + IB4
You are right, I had some troubles with the sign of IB1; and it should be VE1 in my equation, not VB1.

##V_{E1}=I_{C1}/β_{1}.(R_2+R_3)-V_{BE1}=839.29 μA/325 . (22 kΩ+1 kΩ)-0.66 V=-0.60 V##

In my last post I forgot to upload one simulation result (attached here).

Thanks everyone!

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You are right, I had some troubles with the sign of IB1; and it should be VE1 in my equation, not VB1.

##V_{E1}=I_{C1}/β_{1}.(R_2+R_3)-V_{BE1}=839.29 μA/325 . (22 kΩ+1 kΩ)-0.66 V=-0.60 V##
After reading your last post I notice that I also made a small mistake in finding VB1.
As I said earlier the base current enters into the Q1 base. So this means that the current will flow from GND through R2 and R1 and will flow into the base.
So the voltage at Q1 base must be negative VB1 = -Ib1*(R2 + R3) ≈ -60mV and Ve1 = VB1 - Vbe1 = -60mV - 0.61V = -0.67V