# Low pass filter not working properly

This is the pass band that I'm using to filter some EMG signals through electrodes.

When I test it with multisim it works really well as you can see, but when I test it with real equipment (osciloscope and function generator,) the active low filter works fine and the active high filter doesnt work, conversely it shows up -11.8V (around 12V) which comes from the supply voltages. Any thoughts?

The output wave frequency was also distorted. When the input wave was like 5kHz the output wave was like half of 1kHz or less.

EDIT: I had checked the schematic a couple times and already replaced the opamp 3 times.

EDIT #2: The parts that I'm using are the uA741 op-amps.

• Comments are not for extended discussion; this conversation has been moved to chat. Any conclusions reached should be edited back into the question and/or any answer(s). Commented Jan 8, 2020 at 12:10

## Quick Synopsis

Let's quickly summarize what I think I understand. It appears you have the following specifications:

• $$\A_v=10\$$
• $$\f_{_\text{L}}=20\:\text{Hz}\$$
• $$\f_{_\text{H}}=500\:\text{Hz}\$$
• Sallen-Key equal-value component circuits (1-pole, 2nd order)

(I don't have the available voltage rails. But we can ignore that. And we don't need to worry about the opamp, yet.)

First up is to compute a few details in order to see how to arrange the band-pass. There is a serious choice to be made that will be quite different, depending upon the results. This part I think you already know. But it's worth stating, explicitly. So here goes:

• $$\f_{_\text{0}}=\sqrt{20\:\text{Hz}\cdot 500\:\text{Hz}}=100\:\text{Hz}\$$
• fractional bandwidth $$\=\frac{f_{_\text{H}}\:-\: f_{_\text{L}}}{f_{_\text{0}}}=\frac{500\:\text{Hz}\:-\: 20\:\text{Hz}}{100\:\text{Hz}}=4.8\$$

From this last item, I conclude that your approach using a combination of a low-pass and a high-pass filter is correct. Had the fractional bandwidth been a lot less, say below 1 or better still below .8, then there may be an argument instead for combining two bandpass sections, instead. But that's not the case. So you are correct to break things up the way you did.

So far, so good.

## No Input Spec -- Assuming Signal Generator Only

You didn't specify what's driving the system. No, I don't mean the signal generator you used. I mean the real thing that will be driving it when you actually get to making use of it.

Sometimes, you need to AC couple into the filter. If so and if the first section is the low-pass section, you'll need to provide a DC path to ground for the (+) input. I don't see a DC blocking capacitor in your case. And obviously, you didn't need one for the simulation. But I've no idea if you do in the actual circuit. If what's driving this circuit has a DC bias to it, you may very well require DC blocking. Just FYI.

Also, you didn't specify the allowable loading that the first section presents to the actual source. Nor the source impedance, itself. So this means I'm in the dark about these details.

But let's assume for now that this is only a proof that you can do a design and that you'll be using the $$\50\:\Omega\$$ output of the signal generator; with the only purpose in all this is to verify design capabilities.

## Section Order and Other Assumptions

I'm going to just assume you know what you are doing and like the low-pass filter as the first section and want the high-pass filter as the second section. There are considerations, such as the the noise of typical opamps related to their 1/f and bandpass regions, and so on. But I'll just assume you've already made those evaluations and I'll just move on.

I'm also going to assume you are looking for a maximally flat (Butterworth) design. This is important because Sallen-Key equal-value component designs have a fixed relationship between voltage gain and damping ($$\\zeta\$$ or alternately $$\Q\$$.) You don't get to pick the voltage gain if you are looking for Butterworth. If you choose to pick the gain, then you don't get to choose the damping.

Broadly speaking, you have to select a voltage gain less than 3, under all possible circumstances. There's no alternative to that. Since the $$\\sqrt{10}\gt 3\$$, you cannot get $$\A_v=10\$$ with two of these sections. Just can't happen. Adding some gain at the end is okay. But you will need a third section. There's no escaping it.

## Low Pass Design

The low-pass filter has a cut-off at $$\f_{_\text{C}}=500\:\text{Hz}\$$.

Because capacitors aren't usually found in E24 steps, you usually decide on your capacitor values, first. They go in broad steps. In this case, I might select $$\47\:\text{nF}\$$. The nearby resistor value would then be $$\6.8\:\text{k}\Omega\$$. With that combination, $$\f_{_\text{C}}\approx 498\:\text{Hz}\$$. Which is close enough.

The gain of the stage is already set by the required damping to meet a Butterworth filter: $$\A_v=3-\sqrt{2}\approx 1.586\$$. It's determined. You don't get to select it. Sorry.

(The same will be true of the high-pass filter. So we can already say that you will need a final, third section with $$\A_v\approx 4\$$ in order to reach your final goal of $$\A_v=10\$$.)

From this, the low-pass section will be:

simulate this circuit – Schematic created using CircuitLab

(The actual computed value is $$\R_4=22.845\:\text{k}\Omega\$$. But I rounded it down. The price I paid for that is a slightly lower voltage gain of $$\A_v\approx 1.564\$$ and a slight change in the damping. Oh, well. Acceptable.)

## High Pass Design

The high-pass filter has a cut-off at $$\f_{_\text{C}}=20\:\text{Hz}\$$.

In this case, I might select selecting $$\220\:\text{nF}\$$. The nearby resistor value (from E24 series) would then be $$\36\:\text{k}\Omega\$$. With that combination, $$\f_{_\text{C}}\approx 20.1\:\text{Hz}\$$. Which is close enough.

As before, the gain of the stage is already set by the required damping to meet a Butterworth filter: $$\A_v=3-\sqrt{2}\approx 1.586\$$. It's determined.

From this, the high-pass section will be:

simulate this circuit

(Given that both sections had slightly less gain than might have been, ideally, the final, third section will now need $$\A_v\approx 4.1\$$ in order to reach your final goal of $$\A_v=10\$$. A slight adjustment.)

## Summary

At this point, you only need to add a simple section to get close to $$\A_v\approx 4.1\$$. A simple approach:

simulate this circuit

So the final Butterworth result is:

simulate this circuit

And here's LTspice's result from the above schematic (using LT1800's for the opamp choice):

Note that the peak is right at $$\20\:\text{dB}\$$ and where it should be, given your specs.

• Thanks a lot for the awnser. I tested the filters individually and only the Low pass filter is working as supposed due to all the info you mencioned earlier. With that said I just want to know if could I use 1st order filters with a 10 voltage gain to remove the 3rd stage amplifier without having troubles with the Av parameter? Commented Jan 8, 2020 at 12:22
• @FabioEEC Why would you want to attempt that? There will be significant sacrifices? What are your real goals? (It might also be possible to accept a different kind of filter to boost the gain a little of each section. But that ploy can't under any circumstances remove the need for the third section.)
– jonk
Commented Jan 8, 2020 at 22:29
• I'm trying to project a circuit that can control a prosthetic arm using EMG Signals from arm muscles as inputs. The circuit has an instrumental amplifier, then a High pass filter, a low pass band filter, amplifier, sine wave retifier and then a peak detector, the only thing I don't have working is the Band Pass filter with a 10 Voltage gain that my teacher is asking... He didnt mention the amplifier on the band pass filter, he just told us that want a band pass filter with 10V gain... So I'm asking if there's anyway to remove the 3rd stage amplifier with some other type of active filters. Commented Jan 9, 2020 at 0:00
• @FabioEEC Gain and Q are related. To get gain, you'll need high Q. But high Q means narrow bandwidth. You have a wide bandwidth. These things are incompatible with each other with just two sections. You can create a filter with lots more sections and make them higher Q to get higher gain (and some other benefits and downsides that go along with it.) But broadly speaking, the answer is no. Not unless you are willing to go to a larger multi-section filter. And I mean larger. The above is lots easier.
– jonk
Commented Jan 9, 2020 at 0:40
• Alright, Thank you so much for everything! Really apreciated Commented Jan 9, 2020 at 1:16

You need to study the equations for these filters in more depth. Gain has a drastic effect on Q; you cannot make it whatever you like. For an equal R and C circuit, Q=1/(3-G). So the high pass section has a negative Q. Your question also illustrates what a piece of junk most simulators are.

• Darn. I brought this up in a vague question earlier and you nailed what I was thinking, exactly! I'll have to watch you answers more closely! +1 (Of course, I wish you'd write more. I think you could say some useful things. Very nice, though!)
– jonk
Commented Jan 8, 2020 at 8:09
• @jonk. Thank you for your encouraging words. I could write more but I have felt my answers are ignored. Commented Jan 8, 2020 at 8:35
• Well, if I see them they won't be ignored. I'm keeping you in my view, anyway. You nailed this issue exactly. Not just hand-waving crap. But quantitatively. That goes a very long way in my book. It's nice to see someone here who can do that, directly and simply. You have my attention!
– jonk
Commented Jan 8, 2020 at 8:51
• Just FYI. I added an answer that is more along the detailed lines I like to see.
– jonk
Commented Jan 8, 2020 at 9:31