# amplifier circuit help

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

1. ### t_n_k AAC Fanatic!

Mar 6, 2009
5,448
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I suspect the 'best' one could do to at least meet the 10Hz & 10kHz -5dB requirement would be to satisfy the transfer function

$G(s)=-K*\frac{(s+\omega_a)(s+10^4\omega_a)}{(s+100\omega_a)^2}$

Where

$\omega_a=2\pi f_a$

with

$f_a=3.162 \small{Hz}$

& K≈0.165

This gives a 1kHz gain of 13.53dB with the peak gain at 316.2 Hz of 18.33dB

Whether this transfer function can itself be realized using just the four resistor & two capacitor values with one ideal op-amp is debatable.

Last edited: Nov 10, 2011
2. ### uofmx12 Thread Starter Member

Mar 8, 2011
55
0
I made a sine wave with .25Vp at 1kHz with a square wave oscillator and that is the input. Now, I am to create a amplifier ckt, like mentioned in the first post with R4 to the output, that amplifies a 1kHz signal by 25dB or more, but has gain of -5dB or lower for frequencies less than 10Hz and greater than 100kHz. I asked him about using a high pass filter and second order low pass and he said that was not necessary and the one in the original post would work. I am to use the code I provided a few posts up and change the resistors and capacitors to whatever need to make the requirements. I can not get it to work and might possibly try and talk to him more about it tomorrow.

3. ### t_n_k AAC Fanatic!

Mar 6, 2009
5,448
790
As discussed in my last post I have generated a schematic and response which satisfy what I suggested would be the 'best' achievable outcome - having regard to maintaining the desired 10Hz and 10kHz "-5dB" gains. The 25dB gain at 1kHz was not achievable.

The overall circuit Q is nearly 0.5.
The gain at 10Hz is -5.16dB
The gain at 10kHz is -5.25dB
The 1kHz gain is 13.53dB.

The peak gain is 18.37dB at 314.4Hz

Other circuit values can (of course) be used to obtain the same result

For example changing C1 to 330nF one then has C2=20nF, R1=1541.6, R2=152622.7, R3=25182.7, R4=254.37

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• ###### Bandpass part compliant response.png
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Last edited: Nov 11, 2011
4. ### Audioguru Expert

Dec 20, 2007
11,251
1,350
The Q of each of your extremely simple 1st-order RC filters is only 0.5.

Maybe if the lowpass filter is 2nd-order then its slope will be more, its Q will be more and the gain at 1kHz will be more.

5. ### t_n_k AAC Fanatic!

Mar 6, 2009
5,448
790
I realise that. I'm not recommending this as a useful design.

I'm making the point to our fellow member uofmx12 that (notwithstanding their teacher's assurances) I think there's "a snowflake's chance in hell" of achieving the design goal using the mandated circuit topology set out in post #1.

If I'm wrong and end up with "egg on my face" then so be it.

Among others, I eagerly await uofmx12's teacher's explanation of how it has been done.

Probably thatoneguy has made the important point in his post [#20], that some misunderstanding has crept into the problem statement along the way and we aren't getting the entire picture.

Last edited: Nov 11, 2011
6. ### Audioguru Expert

Dec 20, 2007
11,251
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I copied the 1st-order lowpass filter and added a 2nd-order highpass filter. It fits to make a gain of 25dB at 1kHz and 10Hz and 10kHz have gains of -5dB.

• ###### filters again.PNG
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7. ### t_n_k AAC Fanatic!

Mar 6, 2009
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There's no doubting one can readily achieve the design goal without any constraints. In post #4 I show that it is possible with a single op-amp and a lower parts count. Mind you that design exhibits a potentially undesirable dynamic signal (e.g step) response.

The original problem statement of post #1 seems to indicate that this can be achieved with just one op-amp stage and six passive components - at least that's the impression I gain from the OP's various comments. Perhaps I (and others??) have misunderstood and more than one stage is allowed. If that's the case, it's a modest & achievable challenge using the prescribed circuit topology.

8. ### uofmx12 Thread Starter Member

Mar 8, 2011
55
0
Edit: Just realized it was greater than 100kHz. I now have figured it out. WOW!

Sorry for all the confusion, at least I learned a few things through this process and what it would take to make it at 10kHz.

Last edited: Nov 12, 2011
9. ### t_n_k AAC Fanatic!

Mar 6, 2009
5,448
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Wow? - surprise surprise....100kHz.

Worthwhile for the rest of us making sure of your facts in future.

10. ### t_n_k AAC Fanatic!

Mar 6, 2009
5,448
790
Just in case anyone was interested in the final outcome with the updated information I have attached a schematic and associated magnitude plot which meet the revised spec - at least 25dB gain at 1kHz and less than -5dB at 10Hz and 100kHz (not 10kHz as originally stated).

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11. ### thatoneguy Expert

Feb 19, 2009
6,349
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Looks good. What is the output impedance on that, for general edification?

12. ### t_n_k AAC Fanatic!

Mar 6, 2009
5,448
790
Presumably, if the op-amp output resistance is considered as close to ideal then the output impedance would be small (~0Ω). Running the simulation in sensibly loaded [~1kΩ] or unloaded condition seems to make no difference.

Input impedance would be frequency dependent.