- #1

- 139

- 0

## Homework Statement

http://i59.tinypic.com/1smqlu.png

I'm not sure how to calculate differential mode gain

## Homework Equations

I know formuals for CMRR and Acm but not Adm

CMRR = | Adm/Acm |

Rb/Ra = (1-ε)Rd/Rc

You are using an out of date browser. It may not display this or other websites correctly.

You should upgrade or use an alternative browser.

You should upgrade or use an alternative browser.

- Thread starter bnosam
- Start date

- #1

- 139

- 0

http://i59.tinypic.com/1smqlu.png

I'm not sure how to calculate differential mode gain

I know formuals for CMRR and Acm but not Adm

CMRR = | Adm/Acm |

Rb/Ra = (1-ε)Rd/Rc

- #2

gneill

Mentor

- 20,922

- 2,866

Essentially the idea is to define a couple of parameters that represent the differential and common mode inputs in terms of the voltage sources ##v_a## and ##v_b## in your diagram. To wit:

##V_d = v_b - v_a## is defined to be the differential mode input, and

##V_{cm} = \frac{v_b + v_a}{2}## is the common mode input

If you add those two equations together you can find a "new" expression for ##v_a## in terms of ##V_d## and ##V_{cm}##, and if you subtract the first from the second you arrive at a new expression for ##v_b##, also in terms of ##V_d## and ##V_{cm}##. Plug these in for the sources in your circuit and solve your circuit for the resulting output voltage. The site I gave the link for above has more details.

- #3

- 139

- 0

1/2[1000/(1000+1000)] * [(24000 + 25000)/1000 + 24000/25000] = 12.49

So it's exactly half of what the answer should be according to the answers up there? 24.98? Why does it have the 1/2 in front of it? Without it the answer would be 24.98 which would be correct...

- #4

gneill

Mentor

- 20,922

- 2,866

Well let's see. You've used 1000 for R3 when the circuit says it's 24000. You've used 24000 for R4 when your circuit says it's 25000, and 25000 for R2 when your circuit gives it as 1000.

Ad = 1/2[R3/(R1+R3)] [(R4 + R2)/R2 + R4/R2]

1/2[1000/(1000+1000)] * [(24000 + 25000)/1000 + 24000/25000] = 12.49

So it's exactly half of what the answer should be according to the answers up there? 24.98? Why does it have the 1/2 in front of it? Without it the answer would be 24.98 which would be correct...

So, check your resistor placements.

I should mention that just copying a formula and plugging in values is a dangerous way to go. You won't increase your understanding and you'll be left hanging on an exam. You should be able to analyze the circuit and derive the gain from scratch. I don't think you would have made the above mismatch if you laid the groundwork yourself.

- #5

- 139

- 0

1/2(24000/(1000+24000))* ((25000 + 1000)/1000 + 25000/1000) = 24.48

I must have messed up here or something. I remember my prof deriving this for us but he told us we don't need to know how to derive it?

- #6

gneill

Mentor

- 20,922

- 2,866

Lucky you! I never had it so easy :)I remember my prof deriving this for us but he told us we don't need to know how to derive it?

- #7

- 139

- 0

My answer in post #5 seems to be off by .5. I can't spot anything that's wrong

- #8

- 847

- 228

I agree with your result. My calculation givesMy answer in post #5 seems to be off by .5. I can't spot anything that's wrong

Last edited:

- #9

- #10

gneill

Mentor

- 20,922

- 2,866

You and your calculator must have a difference of opinion on the order operations implied by a given key sequence.Where did I mess up? I keep putting it in my calculator and getting it wrong haha

Try breaking down the calculation into smaller units and use memories to store these intermediate values. Then combine the unit results.

- #11

- 139

- 0

1/2(24000/(1000+24000))* ((25000 + 1000)/1000 + 25000/1000)

24000/(1000+24000) = 24000/25000 = .96

(25000+1000)/1000 = 26000/1000 = 26

25000/1000 = 25

1/2 * .96 * (25+26) = 24.48

Drives me insane a little.

- #12

gneill

Mentor

- 20,922

- 2,866

$$A_{dm} = \frac{1}{2} \left[ \left( \frac{R3}{R1 + R3} \right) \left( \frac{R2 + R4}{R2} \right) + \frac{R4}{R2} \right] $$

- #13

- 139

- 0

Yeah that was the issue, thank you :)

$$A_{dm} = \frac{1}{2} \left[ \left( \frac{R3}{R1 + R3} \right) \left( \frac{R2 + R4}{R2} \right) + \frac{R4}{R2} \right] $$

Share: