Hi all,

So I'm trying to make a couple narrowband amplifiers but I'm having a hard time understanding how they're different from just sampling a small portion of a broadband amplifier's response.

So if I'm trying to get 20 dB of gain from say, 100 kHz - 120 kHz. And the gain bandwidth product of the amplifier I'm using is 600 kHz. I build two inverting op amp stages each with a gain of 5. So I'm able to get 20 dB of gain at 120 kHz.

That's how I would do it for a amplifier that amplifies anything to 120 kHz. But I only really need 20 kHz of bandwidth (100 kHz - 120 kHz). So shouldn't I be able to get more gain out of my amplifier, given the small bandwidth?

In theory, It seems like I would be able to get a gain of 30 out of a single stage (600kHz / 20kHz). But something about that just seems odd to me.

I'm just kind of confused on how to do this. Even if I have a filter stage before the amplifier stage and the only signal getting through to the amplifier stage is from 100 kHz - 120 kHz, wouldn't my amplifier still have to work at all frequencies from 0-120 kHz?

Thanks in advance for your help. Any links to further reading on this topic would be much appreciated as well.

 

20dB is gain of 10.
30dB is gain of 31.62
40dB is gain of 100.

These are not extraordinary gains for 0-1MHz amplifiers.
Your amplifier gain does not increase by narrowing the bandwidth.
You can design a narrow band amplifier for 100kHz - 120kHz with 30dB gain.
You can use most opamps with 0-1MHz bandwidth and use low-pass and high-pass active filter design techniques.

Google active filter design.

 

the bandpass of the amplifier does not affect the gain inside the bandwidth. it does affect the noise, narrow band amps are quieter than broadband amps the gain of an amp is specified over the bandwidth of the amp, and is not affected except for roll off near the higher limit and lower limit. if your refering to the gain of a transistor, the gain decreases as the frequency gets higher, the gain bandwidth product reaching 0 at the ft of the transistor.

 

Your amplifier gain does not increase by narrowing the bandwidth.

So I'm right in thinking that the gain of a 0-120 kHz amplifier is that same as a 100 - 120 kHz amplifier? That is to say, when I'm setting the gain of my op amp stages, I would use the same set of resistors in both instances?

It makes sense to me. It didn't seem right that you could just magically get more gain by narrowing the bandwidth. The 100-120 kHz amplifier is, essentially, sampling the response of the 0 - 120 kHz amplifier.

The differences between the two would just be in the amount of noise. I would just need a filter stage between the input and amplification stage to take out the frequencies from 0-100 kHz.

Thank you for your help!

 

You can combine amplification stage and filtering stage. That is what an active filter does.

Think of a filter as attenuating the unwanted frequencies.

You can set the gain of the amplifier to unity and attenuate the unwanted frequencies.

Or you can set the gain of the amplifier to 30dB and still attenuate the unwanted frequencies. So now you have gain in the band-pass region and attenuation in the stop bands.

 

So I'm right in thinking that the gain of a 0-120 kHz amplifier is that same as a 100 - 120 kHz amplifier? That is to say, when I'm setting the gain of my op amp stages, I would use the same set of resistors in both instances?

Yes. The "bandwidth" in gain-bandwidth is the maximum frequency, or bandwidth from DC. So an opamp with a 1 MHz gain-bandwidth product has an open-loop gain of 10,000 at 100 Hz and 1 at 1 MHz. For most voltage-feedback opamps, this is set by an internal single-pole lowpass filter formed by a Miller capacitor around a voltage gain stage as part of the unity-gain compensation scheme.

BTW, if you have two opamp stages in series, each with a gain of 5, the overall gain is 25 (28 dB), not 10 (20 dB).

ak

 

My textbook has definition of broadband bandpass:
You take the upper limit frequency of the bandpass and divide it by lower limit frequency of bandpass, if the answer is 2 or more, then you have broadband condition and you can choose filter topology that is best for broadband.

Example 1.
I want bandpass of my bandpass filter to be from 200 Hz to 500 Hz.
500/200=2.5
2.5>2
Therefore I have broadband bandpass filter.

Example 2.
I am trying to listen to specific signals, these signals occur at frequencies between 350 Hz and 420 Hz.
420/350=1.2
1.2<2
Therefore this is narrowband filter.

 

Some basic theory needs to be investigated before we start to design:
1. A 1MHz GBW op amp has 20dB open loop gain at 100KHz because the gain slope is 20dB per decade. This amp would have very poor gain characteristics.
2. To get a gain of 20dB at 1% you require 40 dB excess gain, so the GBW of the op amp needs to be at least 10MHz better to choose 100MHz because you might be cascading circuits etc.
3. A 120 KHz, 20dB amp will give you the signal level you desire, but the noise contained in the signal and amp from dc to 100 KHz is amplified by 20dB.
4. If you want to eliminate most of the noise precede the amp with a BP filter. Design of Active Filters, with experiments by Howard Berlin is easy to read, but it is not in print so you have to look for it on the web.