# Clarification: Vol.3 Building a Differential Amplifier---Input Impedance

#### User

Joined Jun 16, 2010
4

Stated: "Another limitation of this amplifier design is the fact that its input impedances are rather low...Each input voltage source has to drive current through a resistance, which constitutes far less impedance than the bare input of an op-amp alone. The solution to this problem, fortunately, is quite simple. All we need to do is "buffer" each input voltage signal through a voltage follower"

Why does the addition of a resistor lessen the impedance? Shouldn't it be the other way around?

#### dsp_redux

Joined Apr 11, 2009
182
When you have two paralleled resistors, the equivalent resistance tends towards the smaller one. Exemple, if you have R1||R2 and R1=50ohms; R2=1k, then:
$$R_{eq} = \left( \frac{1}{R_1}+\frac{1}{R_2}\right)^{-1} = 47.6\Omega$$
Same thing apply here. Even if you parallel a high impedance with something smaller, then the resistive effect is inevitably reduces.

#### User

Joined Jun 16, 2010
4
Understood, but wouldnt their equivalent resistance add to the impedance of the op amp input since the resistors are in series with its leads?

#### Wendy

Joined Mar 24, 2008
22,788
Impedance is the sum total of resistance, inductance, and capacitance. Usually the overwhelming number is the resistance.

#### User

Joined Jun 16, 2010
4
Maybe I should be asking the question of how input impedance is measured in an op amp.

#### dsp_redux

Joined Apr 11, 2009
182
Usually, both inputs of an opamp is directly connected to the gate of a FET, or the base of a BJT in a differential pair. On a MOSFET, the resistance seen at the gate is almost infinite (theoretically). See http://en.wikipedia.org/wiki/File:Long-tailed-pair.gif

What you can do to mesure input impedance of the opamp is putting a voltage source in series with a known resistor (preferably near the expected input impedance), and those components in series with the opamp's input. You then mesure the voltage at the opamp's input. Use the voltage divider equation to find the input impedance.

$$V_{IN} = \frac{V_{INPUT} R_{input}}{R_{input} + R_{known}}$$

#### The Electrician

Joined Oct 9, 2007
2,887
The input impedance at the two inputs to the first circuit on the page you referenced:

can be determined by inspection.

If the + and - inputs of the opamp itself are assumed to have such a high impedance that it can be taken as infinite, then the impedance at the V2 input is clearly just 2R. The impedance at the V1 input is easy to determine, because the + input is grounded through a resistance of R which is so low compared to the (essentially) infinite input impedance of the + input of the opamp, that the + input is essentially just grounded. That means that the - input is also a (virtual) ground. Then the input impedance at V1 is just R.

Both these impedances (R at the V1 node, 2R at the V2 node) are very much lower than the very high input impedance of the opamp + and - inputs.