# Differential Amplifier design

Discussion in 'Homework Help' started by Rumination, Mar 25, 2016.

1. ### Rumination Thread Starter Member

Mar 25, 2016
74
1

The figure shows a differential amplifier with a differential input vid = (vin_d_pos - vin_d_neg) between the bases of Q1 and Q2, and an output (out) at the emitter of Q4.

I have to Determine R1, R2, R4, R5 and R6 so that the following requirements are met:

R 1 = R 2
Av = vout / vid = 100 [V / V]
Vout = 0V when Vin_d_pos = Vin_d_neg = 0V.
The output Vout must be able to deliver undistorted peak signal voltage in the range
from vout-min to vout-max with RL armed.
Quiescent current IC = 10 * Q3-Q4 IB

----------
I have been given the values:
Vcc-pos = 21 V
Vcc-neg = 21 V
R3 = 2000 Ohm
RL = 49 Ohm
I1 = 3,56 mA
Vout-max = 8,8 V
Vout-min = -8,8 V
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How can I start? For I have difficulty getting started.

2. ### Rumination Thread Starter Member

Mar 25, 2016
74
1
My English is not so good. I have found this out:

Vcm = 0 , Vin_D = 0
VB1 = VB2 = 0 V.

Ic1 = IE1 = I/2 = 3,65 / 2 = 1,825 mA

VB3 = 8,8 V - R3 * Ic1 = 8,8 V - 2000 * 1,825 mA = 5,15 V.

Ic3 = IE3 = (24 V - VB3 - 0,7 V) / R4

But I don't know the value of R4?

3. ### Jony130 AAC Fanatic!

Feb 17, 2009
3,939
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Hey but, your Vcc-pos is 21 V so VB3 voltage is equal to (if we ignore IB3):
VB3 = 21V - Ic1*R3 = 21V - 1,825 mA*2kΩ1 = 21V - 3.65V = 17.35V
Also notice that R4 and R5 "set" the Q3 voltage gain.
I don't understand this ?

4. ### Rumination Thread Starter Member

Mar 25, 2016
74
1
Yes, you are right. It's 21 V and not 8,8 V. I got confused. But what does this mean:

"R4 and R5 "set" the Q3 voltage gain"?

And just ignore, Quiescent current IC = 10 * Q3-Q4 IB.

5. ### Jony130 AAC Fanatic!

Feb 17, 2009
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The Q3 voltage gain at first glance is equal to AvQ3 ≈ R4/R5

6. ### Rumination Thread Starter Member

Mar 25, 2016
74
1
But I don't know the value of either R4 or R5?

7. ### crutschow Expert

Mar 14, 2008
12,577
3,082
But you know their ratio.
This is not a single answer to their correct values, only their ratio. You select the value to give the desired Q3 transistor bias current.
For a real design this current would affect the frequency response which may be of interest.

8. ### Rumination Thread Starter Member

Mar 25, 2016
74
1
Do you mean:

Ad = gm * Rd ?

9. ### Rumination Thread Starter Member

Mar 25, 2016
74
1
Now I have been working on this problem, but I really can't understand

10. ### Jony130 AAC Fanatic!

Feb 17, 2009
3,939
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You must start at the output. You have been given RL and Vout_max so from there you can find Ic4 and Ic3 quiescent current.
And choose R4,R5R1,R1 to meet the voltage gain requirement at given quiescent current .

11. ### crutschow Expert

Mar 14, 2008
12,577
3,082
What's Rd?
No, that gain equation only holds when there is no emitter resistor.
The emitter resistor provides negative feedback and, for low values of gain (much less than gm*R5), the gain of Q3 is approximately R5/R4.

12. ### Rumination Thread Starter Member

Mar 25, 2016
74
1
Can I do it like this:

VB3=17.35V
We know: VE3=(17.35+0.7)V=21-IC3*R4
We also know: VB4=+0.7V=-21+IC3*R5.
So by eliminating IC3 it gives a second equation for R4 and R5:

18,05 = 21 - R4
R4 = 2,95

0,7 + 21 = R5
R5 = 21,7

Does it mean, that we have found the values of R4 and R5? And now we can find the value of Ic3?

13. ### Rumination Thread Starter Member

Mar 25, 2016
74
1
To find Ic3:

Ic3 = IE3 = (21 V - VBE - 0,7 V) / (R4) = (21 V - 17,35 V - 0,7 V) / (2,95) = 2,95 / 2,95 = 1 mA.

To find VB4:

VB4 = -21 V + R5 * Ic3 = -21 V + 21,7 V * 1 mA = 0,7 V.
Vout = VB4 - 0,7 V = 0 V

To find Ic4:
Ic4 = (0 - (-21 V)) / R6

But I don't know the value of R6.

14. ### Jony130 AAC Fanatic!

Feb 17, 2009
3,939
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But what about Vout-min = -8,8 V and RL = 49 Ohm ? Do you have any info about transistor current gain (beta /hfe) ?
And a tip
Ask yourself a question, why the output voltage is "clip" at -5V ?

15. ### Rumination Thread Starter Member

Mar 25, 2016
74
1
Does it mean, that I can find Ic4:

Ic4 = V / R = 8,8 / 49 = 0,18 mA

16. ### Jony130 AAC Fanatic!

Feb 17, 2009
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Ic4 should be larger than this 0.18mA

17. ### Rumination Thread Starter Member

Mar 25, 2016
74
1
So what am I doing wrong?

18. ### Jony130 AAC Fanatic!

Feb 17, 2009
3,939
1,089
It looks like you do not know (or understand) how to find maximum negative voltage swing at the load for a simply emitter follower circuit (Q4).

19. ### Rumination Thread Starter Member

Mar 25, 2016
74
1
Yes, you are right. I will try and find it in my book. I will be back.

20. ### Jony130 AAC Fanatic!

Feb 17, 2009
3,939
1,089
To help you with this problem look again at my post #14 and Ask yourself -- >What voltage at the T1 base will cut-off T1 transistor?