# amplifier circuit help

Discussion in 'Homework Help' started by uofmx12, Nov 7, 2011.

1. ### uofmx12 Thread Starter Member

Mar 8, 2011
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0
I am trying to make an amplifier circuit, using the first order filter topology, with 4 resistors, 2 capacitors and the opamp.
http://i812.photobucket.com/albums/zz41/uofmx12/Stage2.jpg
I have a 1kHz freq going in along with 500mVpp amp. I am having trouble calculating what the capacitors need to be to make the circuit amplify the signal by 25dB or more but with a gain -5dB or less for any frequency less than 10Hz or greater than 10KHz.

Feb 19, 2009
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3. ### Audioguru New Member

Dec 20, 2007
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896
An input resistor and a negative feedback resistor are used in an inverting opamp amplifier. The ratio of the resistors sets the gain.
The series input capacitor is calculated for the highpass filter with the input resistor and the parallel feedback capacitor across the feedback resistor is calculated for the lowpass filter.

The calculations for the capacitors give an output which is -3dB (0.707 times) so the gain at 10Hz and at 10kHz is (25 x 0.707=) too much. You want the gain to be 30 times less. Then the highpass and lowpass cutoff frequencies will be the same and the simple filter needs to be much more than first-order.

The bandpass filter shown will work but uses more parts than you are allowed to use.

4. ### t_n_k AAC Fanatic!

Mar 6, 2009
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It is possible to achieve the 'design goals' using a single stage MFB topology.

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5. ### uofmx12 Thread Starter Member

Mar 8, 2011
55
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Ok, so for what I did have I see that I can not get my gain higher than what i have it. Here are the values I have now and what is displayed using the circuit in the first post with R4 connected to the output. Is there a way to use the first order filter topology or will I have to use t_n_k design? Someone mentioned needing a second order low pass filter but not sure implementing it and the values then.

R1=.4e+3;
R2=24e+3;
R3=7e+3;
R4=.09e+3;

C1=1000e-9;
C2=8.5e-8;

6. ### JoeJester AAC Fanatic!

Apr 26, 2005
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Your graph does not meet the design specifications you mentioned in the first post.

7. ### t_n_k AAC Fanatic!

Mar 6, 2009
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782
Hi uofmx12,

You'll most likely never meet the spec with your topology.

There are two real poles and two real zeros.

The two poles are ideally near & symmetrical with the target center frequency [1kHz]. The low frequency zero causes the output to rise from the low frequency end. The center poles cause the output to roll off as one increases frequency above the center frequency. The roll off can only at best be ~-20dB per decade. You have to drop 30dB in a decade from 1KHz to 10kHz- it most likely won't happen. I guess you can shift the center frequency lower than 1kHz to get the 10kHz gain down - as you appear to have done - but then you have to boost the overall gain to achieve the 25dB gain value at 1kHz.

I think you will always be fighting these conflicting requirements. I'll certainly be interested to hear if it can be achieved with your topology.

8. ### uofmx12 Thread Starter Member

Mar 8, 2011
55
0
Thankyou for stating the obvious. I mentioned that in the post and the reason I showed my calculations. Also the reason I am posting this thread as in need of help.

9. ### uofmx12 Thread Starter Member

Mar 8, 2011
55
0
In your graph, I see you used a MFB Band pass. Looking at the formulas, I am not sure how you got your values of resistors. For fm=(1/2piC)*sqrt([R1+R3/(R1R2R3)]) and the gain at fm=R2/2R1. Also, how you came up with the plot.

Would I be able to use a second order low pass filter to get my results? I was informed that it might be the case and would help to get a gain greater than 20dB.

just not familiar with it but I know the general equations for gain, R1-R3, etc just now sure how to make it fit my requirements.

Last edited: Nov 9, 2011
10. ### t_n_k AAC Fanatic!

Mar 6, 2009
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If you are constrained by the component + OP-AMP count per your original post - no I don't think that would work. I may have misunderstood your question here however.

The MFB bandpass design is a little convoluted but not particularly difficult.

For the attached generic schematic the 's' domain transfer function is given by

$A_v=-\frac{\frac{\large{s}}{R_1C_1}}{s^2+\frac{(C_1+C_2)}{C_1C_2R_3}s+\frac{1}{C_1C_2R_3}$\frac{1}{R_1}+\frac{1}{R_2}$$

This has the generic form

$A_v=-\frac{H\omega_0 s}{s^2+\frac{\omega_0}{Q}s+\omega_0^2}$

One makes the following operations found from typical MFB filter analyses you can find on the web.

Gain at ω0 is Av(ω0)=Q*H , where Q is related to the response damping ['Q' factor], H is an intermediate gain-related term.

If the gain is 25dB at 1kHz then |Av|=17.783 at 1kHz

So Av=H*Q=17.783

One needs a Q of ~3.5 to meet the 10Hz & 10kHz gain requirement of less than -5dB - again you find this by trial and error.

So H=17.783/3.5=5.08

One now proceeds as follows

Let C=C1=C2=22nF say [ again these values are 'found' through trial and error. C=22nF gives 'sensible' resistance values]

Let k=ω0*C=6283*22E-9=1.382E-4

R1=1/(H*k)=1/(1.382E-4*5.08)=1424 Ω

R2=1/[k*(2Q-H)]=1/[1.382E-4(7-5.08)]=1/2.653E-4=3769 Ω

R3=2*Q/k=7/1.382E-4=50.65 kΩ

The attached simulated magnitude vs frequency response was derived from a simulation of the circuit with calculated values - using software SIMETRIX.

You could also generate the Bode magnitude plot of the 's' domain transfer function [Av] using Matlab or something similar - I use an application called Scilab. I also used Scilab to determine the minimum Q needed to satisfy the 10Hz and 10kHz gain stipulation.

• ###### MFB Bandpass Generic.png
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11. ### uofmx12 Thread Starter Member

Mar 8, 2011
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thankyou for the detailed explanation. The plot is what I am looking for and meets the requirements. Not sure if the circuit will be of use as, my understanding, I am able to do it with the original circuit in the first post but I was unable to do that. I will hopefully have it figured out soon and hopefully be able to use the second order low pass.

12. ### Audioguru New Member

Dec 20, 2007
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The original circuit in the first post has no negative feedback and no power supplies so it doesn't work.
If it has negative feedback and power supplies then its simple 1st-order filters have slopes that are too gradual at 6dB per octave to meet your requirements.

2nd-order filters have a slope of 12dB per octave but then the circuit will be much more complex.

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13. ### uofmx12 Thread Starter Member

Mar 8, 2011
55
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Well, the circuit is not 'complete'. I forgot to connect R4 to the output and also the power supplies. When use the equations in matlab as far as gain, impedance, etc for the 6 values...in post #5 is what I could get as for as my dB at 1kHz which is about 17dB, when I need 25dB.

14. ### Audioguru New Member

Dec 20, 2007
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Your 1st-order filters have slopes that are too gradual for more gain at 1kHz.
2nd-order filters have a steeper slope so would allow more gain at 1kHz.

15. ### t_n_k AAC Fanatic!

Mar 6, 2009
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Who initially told you it could be done? The person who proposed this as the challenge problem - a teacher / tutor? Or is this something you are just working on as a matter of interest?

16. ### uofmx12 Thread Starter Member

Mar 8, 2011
55
0
teacher assistant said it was possible, as I was reassured again today. The code I am using the adjust the resistors and capacitors is:
Code ( (Unknown Language)):
1.
2. f1=1:1e+6;
3.
4. Ra=2300;
5. Rb=80000;
6. Rc=38000;
7. Rd=1000;
8.
9. Ca=100e-9;
10. Cb=20e-9;
11.
12. Zca=1./(1i*2*pi*f1*Ca);
13. Zcb=1./(1i*2*pi*f1*Cb);
14.
15. Zin=Ra+Rb*Zca./(Rb+Zca);
16. Zf=Rd+Rc*Zcb./(Rc+Zcb);
17.
18. g1=-Zf./Zin;
19. G1=20*log10(abs(g1));
20.
Then use semilog to plot.

These values I have in there show the correct gain for <10Hz and >10kHz but can't get the gain above 25dB at 1kHz.

17. ### t_n_k AAC Fanatic!

Mar 6, 2009
5,448
782
Well we'll hopefully see how the design goals are achieved once your assignment is submitted.

Again, at the risk of stating the obvious, with the latest values you have successfully achieved the required <-5dB at 10Hz and 10kHz but your 1kHz gain is well short of 25dB at 9.1dB. The gap of 15.9dB is a reasonable hurdle to overcome.

18. ### uofmx12 Thread Starter Member

Mar 8, 2011
55
0
Yea, that is what I have now. But by changing the resistor values and capacitor values the requirements are supposed to make.

19. ### Audioguru New Member

Dec 20, 2007
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896
You cannot change the slopes of your simple 1st-order filters. But by changing the resistor or capacitor values then the frequencies where the gain is -5dB can be moved apart for more gain at 1kHz.
Try it with 4.2Hz and 22kHz.

20. ### thatoneguy AAC Fanatic!

Feb 19, 2009
6,357
718
Can you do us a favor and post what the profs' solution to the question was once you find out?

I also don't see a way with the components you have, unless there's a trick I haven't seen, or the desired outcome was mis-worded.