Opamp with DC gain of 1 (but a 10x AC gain) - Page 1
Forum section: electronics / beginners

author: maelh
author_rank: Regular Contributor
timestamp: December 17, 2022, 09:03:11 pm
content: Hello,As mentioned in a previous topic, I found the following solution to limit the DC gain to 1.Source:https://electronics.stackexchange.com/questions/191672/how-to-remove-the-dc-offset-in-a-cascaded-op-amp-amplifier-circuit/191677#191677Why does adding a capacitor between the 100 Ohm resistor and ground limit the DC gain to 1?Is it acting like a voltage divider? Or is R3 and C1 acting like a RC low pass filter and shorting this to ground? How to choose a good capacitor value and does it affect the AC gain?Could someone explain how this limits the DC gain in more detail?

author: Psi
author_rank: Super Contributor
timestamp: December 17, 2022, 09:06:25 pm
content: The output through R2 and R3 and ground form a voltage divider.So the output is reduced and fed back in to the input.Therefore the opamp has to amplifier the output by an amount to make everything balance again.If you add a capacitor into the voltage divider it becomes useless for DC since DC cant flow through a capacitor to ground so the voltage divider doesn't work.You effectively have R2 linking output to input and hence a gain of 1 (for DC).But AC can flow through the capacitor and make the voltage divider work. So you get AC gain but no DC gain.

author: MrAl
author_rank: Super Contributor
timestamp: December 17, 2022, 10:57:04 pm
content: Quote from: maelh on December 17, 2022, 09:03:11 pmThere are a couple things about that second circuit that are interesting.First, the AC gain acts like a high pass filter, so for higher frequencies the gain is about 10, and for lower frequencies the gain is between 1 and 10.For DC it is 1 because then we can consider the cap to be 'open'.The other thing is that during startup with a DC input of 1v, the output will start at about 10v and gradually drop down to 1.The formula for the AC gain is:sqrt(4.0e-4*pi^2*f^2+1)/sqrt(4.0e-6*pi^2*f^2+1)and the transient response is:Vout=Vin*(9*e^(-1000*t)+1)You can check out those formulas for more info.

author: Terry Bites
author_rank: Super Contributor
timestamp: December 21, 2022, 12:40:33 pm
content: No Current flows in the cap at DC. Current flows in the cap when AC is present.Just follow usual opamp rules.Of course the AC gain depends on the C1.R3 product. If Xc is much lower than R3 at your minimum frequency then you can ignore Xc.This circuit is very handy when you have only a single supply and you need to bias the output to Vcc/2.

author: TimFox
author_rank: Super Contributor
timestamp: December 21, 2022, 06:41:29 pm
content: The circuit with the series capacitor is very useful in, for example, audio amplifiers.Note that the 10 uF capacitor will have a self-resonant frequency, perhaps 100 kHz for a film capacitor (depending on dimensions).Above that frequency, the reactance will increase and change the high-frequency AC gain a bit (minimum reactance would be < 1 ohm before the increase in inductive reactance for 100 kHz SRF and 10 uF).That effect must be compared to the 100 ohm resistor in the original example.