Simple op-amp Circuits

Op-Amp (Operational Amplifier) is a fundamental building block for handling analog electrical signals.
An operational amplifier is a high gain, differential, voltage amplifier.
OP AMP has two inputs called “+” and “-,” ( or V_IN+ and V_IN-) and a single output.
The output depends only on the difference of the voltage on the two inputs.
If the difference of the two input voltages is V_IN , the output voltage is V_Out, then V_Out = ΔV_IN G_V; where G_v is the (voltage) gain.
Differential operation involves the use of opposite polarity inputs.
Common mode operation involves the use of the same polarity inputs.
Common-mode rejection compares the gain for differential inputs to that for common inputs.

Properties of Op-Amp Op-Amp Classification

Differential Operational Amplifier:

A differential operational amplifier has inverting and non-inverting inputs with high input impedance and differential or open-loop gains between 1000 and 10 million.
When the inverting input is used with negative feedback due to R₀, the closed loop gain is given by (-R₀ / R₁) and the input impedance is R₁ the output impedance is the open loop output impedance divided by loop gain.

Loop gain (dB) = Open loop gain (dB) – Closed loop gain (dB)

If a number of signals are connected to the inverting input, the output is proportional to the sum of the input signals, making possible the solution of linear algebraic and differential equations on an analog computer.
If the non-inverting input to a differential operational amplifier is used, the input impedance is increased to a value,

R_cm || (R_i × loop gain)

where R_cm is the common mode impedance and R_i is the differential impedance.

One way to increase input impedance to an amplifier utilizing the inverting input is to reduce the feedback voltage by connecting a voltage divider at the output.
The voltage gain for a non-inverting input is:

A true ideal differential amplifier the difference between two input voltages providing an output,

In practice, the output also consists of an error term that is due to the common-mode input voltage = (V1 + V2)/2.
Total output of a differential amplifier is:

Common Mode Rejection Ratio (CMRR)

The common mode rejection ratio is a figure of merit of a differential amplifier, since it is the ratio of differential gain, A_d (the desired gain), to the common-mode gain A_C.

Emitter-coupled differential amplifiers are the type of circuit used predominantly in IC_s, because of the manufacturing ability to closely match components, and since the devices are so closely spaced their variations due to temperature tend to cancel, providing excellent DC coupling stability.
High values of CMRR are provided by large effective values of emitter resistance Re, in the emitter-coupled amplifier. This may be provided by a transistor or CRD to provide essentially a constant-current source in the emitter.

Ideal Voltage Transfer Curve:

The graphic representation of the output equation is shown in figure in which the output voltage V₀ is plotted against differential input voltage V_d, keeping gain A_d constant.