# Maximum AC gain of active lowpass filter (integrator)

#### Ahura Mazda

Joined Aug 18, 2018
4
Hi everybody!

I am asking this question because I am stuck at the moment. We have to optimize the given circuit in OrCAD Optimizer, but i just cannot achieve the criteria. Before optimization with values given, maximum AC voltage amplitude gain was around 60 dB, but for no values chosen for R and C will it increase. (I should try to reach 70 dB.)

Given this is an integrator, lowering capacitance at least should increase the amplitude, but id doesn't. Is it a trick question because LT1001/LT is not capable of such amplification or am I missing something? Also, increasing supply voltage does nothing.

I have tried other op-amps and the differences of transfer functions can be seen, but what is explanation?

This is the circuit:

Just .PARAM for C value.

I would greatly appreciate any response! Thank you.

Joined Mar 10, 2018
4,057
Is that a 20 ohm load on output ? LT1001 cannot drive 20
ohms.

Regards, Dana.

#### Ahura Mazda

Joined Aug 18, 2018
4
Is that a 20 ohm load on output ? LT1001 cannot drive 20
ohms.

Regards, Dana.
First of all, thank you for answering.

And, wow. You are right! Increasing the load improved the transfer's function maximum value. But, may I ask why? How does one know?

In any way, again, thank you immensely.

Last edited:

#### Audioguru

Joined Dec 20, 2007
11,249
The datasheet of the LT1001 opamp says its voltage gain is guaranteed if its output current does not exceed 10mA. Into 20 ohms the max allowed output voltage is only 10mA x 20 ohms= 0.2V peak.

Your schematic does not show a frequency. The opamp has a max gain of 1000 (60dB) at 1kHz.

#### Ahura Mazda

Joined Aug 18, 2018
4
The datasheet of the LT1001 opamp says its voltage gain is guaranteed if its output current does not exceed 10mA. Into 20 ohms the max allowed output voltage is only 10mA x 20 ohms= 0.2V peak.

Your schematic does not show a frequency. The opamp has a max gain of 1000 (60dB) at 1kHz.
Well, i did a frequency response, the frequency is variable. Anyways, that clarifies it a lot. It all makes sense now.

Highly appreciate your help. Thank you, Audioguru.

#### MrAl

Joined Jun 17, 2014
8,548
Hi,

Once you get things working you should see a 70db gain at around f=22 Hz if the op amp can go that high. Once you go over that in frequency the RC values shown in the schematic will lower the gain. For example at around 71Hz the gain will be down to 60db and that is with an ideal op amp and of course appropriate load.

#### Ahura Mazda

Joined Aug 18, 2018
4
Okay, now i have another question. After running a few simulations, i observed that there is a threshold after which increasing Rout no longer improves transfer function, and it's maximum lowers with value of Rout. So, even though the current is now much smaller than the limit for guaranteed voltage gain, something else is affecting it.

I've been looking at output voltage swing, thinking that if it was lowering, than overall gain would be lowering too, but with Rout increasing, here we see it is constant. Which makes sense.

Here is AC analysis with R=1.5k, C=1.5n and .PARAM for Rout. (Values at higher frequencies are quite similar.)
Purple – 800 ohms;
Red – 400 ohms;
Yellow – 1k;
Purple – 2k;
Green – 20 ohms.

I'm just curious how to quantify this.

#### MrAl

Joined Jun 17, 2014
8,548
Hi,

There is always some non zero output impedance you could try that idea. That will mean you'll see a decrease in output with decreasing output load resistance.
Add some output impedance to your hand circuit analysis and see what you can come up with.
The limit of the purple at 1Hz is roughly the max gain with roughly zero output impedance so you can use that as a starting point.
You find the max internal gain then add some output impedance and that should show some results.

Joined Mar 10, 2018
4,057
If you do an s plane analysis of Zout opAmp you will find it looks
inductive, eg. as G drops, result of its AC response, the ability to keep
Zo low evaporates, and it rises as frequency goes up.

It s a fun exercise to take a single pole comped OpAmp and do s
plane on Zin, Zout, Vritual Ground response.......

Regards, Dana.