Op-amp amplifier with 10 dB/decade non-linear frequency response? - Page 1
Forum section: electronics / projects

author: Dago
author_rank: Frequent Contributor
timestamp: May 14, 2015, 08:08:31 am
content: Here is a little puzzle for you guys. I have a need for an op-amp amplifier stage which has a non-linear frequency response. The amplifier should have 20 dB/decade of amplification as a function of the frequency. The issue with this is that if I do it with one stage I end up with a boatload of gain (around 50 dB for the top end) if my bandwidth is something around 1-500 kHz. AFAIK I should try to avoid such high amounts of gain for one stage because it will make the amp prone to oscillation and sensitive to noise.I could split the gain to two stages if I could have two stages with 10 dB/decade gain change. But is it possible to make such an amplifier? Any other ideas how to do this?Here is something I've come up so far:I am not 100% sure on the total amount of gain needed yet but it will be quite a bit. Probably something in the range of 40-85 dB. Also not totally sure on the balance between attenuation of the low frequencies and gain of the higher frequencies but I can always change that with the component values.

author: Kalvin
author_rank: Super Contributor
timestamp: May 14, 2015, 08:24:09 am
content: Pink noise [low-pass filter] has -10dB/decade slope and it can be realized using an opamp and a few RC-components. So I guess, it should be quite easy to convert it to a +10dB/decade high pass filter.

author: Kleinstein
author_rank: Super Contributor
timestamp: May 14, 2015, 08:55:14 am
content: A first order filter has 20 dB/decade. There is no simple way to get 10 dB over a larger range. It might be possible to split the amplification in 2 frequency ranges and adjust them, so there is a nearly continuous 20 dB slope also in the overlap range. So a one stage might give the 20 dB/decade from something like 1 - 10 kHz and a second from 50-500 kHz. In between there will be combination from both stages. But I don't think this will help very much.Building a differentiator is always tricky - you have to accept an upper frequency limit where the signal no longer increases, as there is no such thing as ever increasing amplification. Its likely more practical to start design at the upper limit and set a reasonable amplification there (e.g. 10 times). This will naturally lead to an amplification of less than 1 at the lower frequency range.The circuit would likely need a resistor (e.g. 50 Ohms) in series to C1. Otherwise the source or amplifier stage before that will have trouble too with a capacitive load.

author: tggzzz
author_rank: Super Contributor
timestamp: May 14, 2015, 08:56:05 am
content: Quote from: Dago on May 14, 2015, 08:08:31 amThat is a very oddly-phrased specification. Can I suggest you draw a picture of what you want, and preferably why you need it.

author: Kalvin
author_rank: Super Contributor
timestamp: May 14, 2015, 09:08:27 am
content: Here is discussion of the pink noise filter and its realization:http://www.poulpetersen.dk/xfiles/cir/gbpinkfi.htmlWith proper frequency scaling of the component values and low-pass to high-pass conversion, one should get a decent +10dB/decade slope. Please make sure to check the phase response if that is important.

author: T3sl4co1l
author_rank: Super Contributor
timestamp: May 14, 2015, 09:26:12 am
content: I don't think this is a -10dB/dec pink noise filter...Can you say anything about the application?Tim

author: Kalvin
author_rank: Super Contributor
timestamp: May 14, 2015, 09:46:01 am
content: Quote from: T3sl4co1l on May 14, 2015, 09:26:12 amI don't either, and commented only as the pink [low-pass] filter has -10 dB/dec slope in the given bandwidth, so it should be possible to make a similar high-pass filter with a +10dB/dec slope:Quote from: Dago on May 14, 2015, 08:08:31 amedit: SECTION 5-5: FREQUENCY TRANSFORMATIONShttp://www.analog.com/library/analogDialogue/archives/39-05/Web_Ch5_final_PtB_F.pdf

author: Dago
author_rank: Frequent Contributor
timestamp: May 14, 2015, 11:07:44 am
content: Quote from: tggzzz on May 14, 2015, 08:56:05 amThe picture portrays the kind of response I want. Just not sure if it is a good idea to implement in one stage because it has over 50 dB of gain in the top end. To split it two to successive stages each stage would need to have a 10 dB/decade increase in gain to get a total response like the one I showed. This is the second IF-amplifier for a frequency modulated continuous wave radar. The echos closest to the antenna will result in lower frequency, and the signal amplitude drops as a function of the distance. Thus to maximize the dynamic range of the system you need more amplification for the higher frequencies than for the lower ones.

author: Kalvin
author_rank: Super Contributor
timestamp: May 14, 2015, 12:50:09 pm
content: Here is a simulation of the +10dB/dec slope prototype. It is quite easy to finetune the low frequency and high frequency knees.

author: T3sl4co1l
author_rank: Super Contributor
timestamp: May 14, 2015, 01:12:14 pm
content: Ah, OK.To break that down, you're more likely to do better with a step pyramid of band-boost/hi-pass stages.Since radiation is inverse-square law, why not +40dB/dec? Or since reflected radiation is inverse-fourth, why not +80?If your gain is not very particular, you might also be better off with a small capacitor coupling to a discrete transimpedance amplifier. You can get much better fT and noise figure that way.Very quickly, one way or another, you're going to run into noise problems, and you'll want to use another method, like a multi band log detector (think spectrum analyzer). Each band has all the gain it wants, and adjusts to as much as it needs. Or given enough sampling and dynamic range, it can be done with an FFT as well.Tim

author: tggzzz
author_rank: Super Contributor
timestamp: May 14, 2015, 02:31:13 pm
content: Quote from: Dago on May 14, 2015, 11:07:44 amSo, you actually want a linear filter.Is the flat -20dB gain at <100Hz important?Given that the DC gain is <1, you might want to check the loop stability; some opamps can be fussy in that way. In addition, before relying on a simulation model too much, it is wise to verify what the model does and doesn't include.As noted by others, you might be able to avoid all the problems by using a logarithmic amplifier; Analog Devices makes a range of them.

author: macboy
author_rank: Super Contributor
timestamp: May 14, 2015, 03:01:19 pm
content: Cacase two shelving high-pass filters. The shelving high pass will limit the maximum cut/gain of each stage. The first one can provide gain on the first 1.5 decades, and the second one on the next 1.5 decades.

author: Dago
author_rank: Frequent Contributor
timestamp: May 15, 2015, 02:27:45 pm
content: Quote from: T3sl4co1l on May 14, 2015, 01:12:14 pmThanks for all the suggestions! Good that you mentioned the inverse law, it got me thinking. But the _power_ of reflected radiation goes down 1/r^4 which is 40 dB/decade. But the received _voltage_ only goes down 20 dB/decade<- Edit: No, wrong, it is of course 40 dB/decade still because of 20*log etc.I also redid some of my calculations and figured I can drop down the bandwidth a lot (no use amplifying such high frequencies which correspond to very long distances where my sensitivity is not going to be enough anyway) so doing it in one stage should be feasible.