# What is the input impedance of this circuit?

Here is the relevant part of the schematic of the Befaco InAmp, a Eurorack preamp for line level and instrument level signals:

I am trying to determine whether I can safely connect the AKG c1000S microphone to it, which has a 200Ω output impedance and, according to its manual, requires a preamp with at least 2000Ω input impedance.

Since the value of resistor R2 is 100k, can I assume that the input impedance is 100k? Since that is a lot higher than required, will that mean that my mic volume will be too low? Finally, could I use a passive transformer to increase the output impedance of the microphone before connecting it to the InAmp? Or is the only solution to use a dedicated mic preamp?

The impedance is the ratio between the voltage of the input and the current which pass through. It would be R2 if R2 was connected directly to the ground. Here, R2 is connected to R3 which is connected to the output of the operational amplifier.

The output is at Vout = - Vin . R3/R2. (This is the voltage which makes equal the input levels of the operational amplifier).

The current is I = (Vin-Vout)/(R3+R2) = Vin (1+ R3/R2) / (R3+R2)

Then the impedance Z = Vin / I = (R3+R2)/(1+R3/R2).

I consider the case in which the capacitors has a null impedance… if it is not the case, we should take into account the frequency.

EDIT : developping Z = (R3+R2)/(R2+R3).R2 = R2… Then you where right. I could have infer it sooner (the right end to of R2 is not connected to the ground but to « other things which makes its voltage null », then it is as it was connected to the ground.

• Thanks for the formula! From it, I deduce that the impedance cannot be calculated without knowing R3, correct?
– Jaap Joris Vens
Commented Nov 20, 2021 at 10:43
• tbh, though I know very little about actual electronics, I'd have gone with the simpler explanation of "It's a line input. You'll need a mic preamp to not only match the impedance but also lift it to line level."
– Tetsujin
Commented Nov 20, 2021 at 10:50
• Where is R3? Is it not visible in this snippet of a larger schematic? If it happens to be a feedback resistor from the output of the opamp to the inverting input, then the opamp circuit is the common inverting amplifier configuration. If that is the case, then the inverting input is a virtual ground and the input impedance is equal to 100k (R2) rising at low frequencies due to C5. Commented Nov 20, 2021 at 15:19
• @SupaNova, it's exactly that. The full schematic PDF is there on the linked page. Commented Nov 20, 2021 at 22:40

It looks like the op amp has negative feedback so there is a "virtual short" between the inverting and non-inverting inputs. Therefore, the inverting input is also at ground and the minimum input resistance is equal to R2, 100 k$$\\Omega\$$. The impedance will be higher at low frequencies where the reactance of C5 starts to become significant.

• Yes, a « virtual shortcut » a nice image… as I have said, I should have think about it at the first writing. I have edit it with « other things which makes its voltage null », then a « virtual ground » if I copy your v word. Commented Nov 20, 2021 at 22:53

The input impedance of the amp is indeed about 100 kΩ but that isn't why the audio level will be too low. It's because the amp is specified for line level input. The linked page suggests domestic line level which is typically ~316 mV (-10dbV) but your mic is specified for 6 mV at 1 Pa (= 94 dB = someone bellowing into it at close range).

You could try a mic transformer but a 2 kΩ to 100kΩ transformer will only boost the signal to 42 mV. A better option is a microphone preamp which will be able to provide low noise amplication of your mic signal up to line level. It will also provide a balanced input for reduced electrical interference with longer XLR cables. You can opt for one with phantom power to save fitting batteries in the mic.

When an Opamp is at "operating" conditions, its inputs are driven to the same voltage. So the input impedance is essentially 100k as long as the frequency is significantly above the corner frequency of the RC highpass. Corner frequency is 1/(2 pi RC) which is a bit above 7Hz, so the impact of the capacitor on the input impedance should be negligible at audio frequencies.

An input impedance of 100k is quite a bit of impedance mismatch so your results may end up noisier than necessary. A 1:7 transformer could match 2k to 100k and give you about 17dB more signal level in theory. Practice is always a bit different but in case you find your signal too quiet in relation to the amp noise levels, this may be the easiest way to improve the results.

• Just to clarify, the inputs can be assumed to be at the same voltage only if negative feedback is used and the output has not saturated. Commented Nov 20, 2021 at 18:18
• Based on your answer, I connected the 0.2K microphone to the 100K input and the results were exactly as you predicted: low signal and high noise levels. No black smoke. I'm curious to see whether an inline impedance converter will really boost the signal by 17dB. I ordered one and will report back here with the results. If you'll allow me a followup question: what would happen if I chained the two preamps together? Black smoke? Commented Nov 20, 2021 at 19:40
• @JaapJorisVens "two preamps" = if you mean two of the Befaco amps you'll get more signal but even more noise. Commented Nov 21, 2021 at 1:47
• The Befaco contains 2 separate preamps. I meant connecting he output of the first preamp into the input of the second. I tried it, and indeed I only got more noise ¯\_(ツ)_/¯ Commented Nov 21, 2021 at 17:06