Memo: Op-amp’s analog characteristics

Operational amplifier (op-amp) possesses an open-loop gain factor A0 and a close-circuit gain factor A.

The negative terminal of the op-amp is called “inverting” terminal and the positive terminal is called “non-inverting”. In addition to two input terminals, there are two power terminal V+vcc and V-vcc.

The output Vout is calculated as

Vout = A * (V+in – V-in).

The ideal op-amp has the following characteristics:

Input impedance rin approaches infinity.

Meanwhile, output rout impedance approaches zero.

Unity gain amplifier

These characteristics see applications in voltage follower (also known as unity gain amplifier), which produces an output voltage equal to input voltage but with much lower impedance. Low impedance circuits allow more current draw than high impedance ones.

Voltage follower setup: a simple negative feedback loop without any resistance

This unity gain is possible because the gain factor used here is open loop

Vout / Vin = A/ (1+A0)

as Aapproaches infinity

Vout / Vin = 1

Gain of closed-loop amplifiers

In other cases, the gain is determined by the values of the voltage divider overlaying the feedback loop. For example

A non-inverting amplifier: negative feedback with voltage divider setup

In this case, the gain is determined using Kirchhoff’s law. Since Kirchhoff’s current law states that the same current must leave a node as enter it and since the impedance into the (−) pin is near infinity, we can assume practically all of the same current i flows through Rf, creating an output voltage

{\displaystyle V_{\text{out}}=V_{\text{in}}+i\times R_{f}=V_{\text{in}}+\left({\frac {V_{\text{in}}}{R_{g}}}\times R_{f}\right)=V_{\text{in}}+{\frac {V_{\text{in}}\times R_{f}}{R_{g}}}=V_{\text{in}}\left(1+{\frac {R_{f}}{R_{g}}}\right).}

Finally, we have the following closed-loop gain (applicable only to the above circuit)

{\displaystyle A_{\text{CL}}={\frac {V_{\text{out}}}{V_{\text{in}}}}=1+{\frac {R_{f}}{R_{g}}}.}

High-frequency characteristics

The gains and formulas above are only applicable for low-frequency circuits. In high frequencies, the following will happen:

Above certain frequencies, voltage gain and current gain factors become diminished in inverse proportion to frequency increase.

The output signal becomes lagged behind the input signal (phase shifting) as the op-amp cannot react fast enough to the frequency changes.

Very high input amplitude (peak-to-peak voltage swing of the electrical signal) causes distortions and the higher the frequency, the lower this upper amplitude threshold is (distortion appears at lower amplitudes at high frequencies).

The cut-off frequency is the frequency at which the voltage gain is 1/sqrt(2) of the low-frequency gain, meaning, the power at the output is effectively halved in voltage follower setup. The cut-off frequency is unique to each op-amp component. It can be easier determined using an oscilloscope as the frequency at which the phase shift is 180o.

Textbook definition:

The frequency where the voltage falls to 0.707 of its intended value is the cutoff or -3 dB frequency, fc. (Gain in decibels = 20∙log(0.707) = -3dB.)

As a result of these special high-frequency characteristics, op-amps can be unsuitable for high-frequency applications.

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