Operational Amplifier

An Operational Amplifier is an integrated circuit that produces an output voltage Vo that is amplified replica of the difference between two input voltages V1& V2. It is a direct coupled high gain amplifier to which feedback is added to control its overall response characteristics. It is used to perform a variety of linear functions (also some non-linear operations). It offers all the advantages of monolithic integrated circuit: small size, high reliability, reduced cost, temperature tracking & low offset voltage & current.

The Op-Amp parameters are classified as AC & DC parameters.

**AC Parameters:**

1) Frequency response

2) Slew Rate

3) Common Mode Rejection Ratio (CMRR)

4) Frequency compensation

5) Stability

**DC Parameters:**

1) Input Offset Voltage(Vio)

2) Input Bias Current(IB)

3) Input Offset Current(Iio)

4) Thermal drift

**Common Mode Rejection Ratio (CMRR) :**

The relative sensitivity of an op-amp to a differential signal as compared to common mode signal is called as CMRR & gives the figure of merit of the differential amplifier.

Mathematically CMRR is defined as the ratio of differential voltage gain to common mode gain of an op-amp.

**For an ideal op-amp, ρ = ∞ **

** For IC LM 741, ρ = 90 dB**

** For IC LF 356, ρ = 100 dB**

**Slew Rate (SR):**

It is defined as the maximum rate of change of output voltage with time. It is generally specified in V/µs. It is also useful to determine the maximum allowable input frequency.

It is defined as

SR= dVo/dt

Slew rate is caused by current limiting and the saturation of internal stages of op-amp when a high frequency, large amplitude signal is applied. The resulting current is the maximum current available to charge the compensation capacitance network.

We know that capacitor requires a finite amount of time to charge and discharge. This means the internal capacitors prevent the output voltage from responding immediately to a fast changing input. The rate at which the voltage across the capacitor is the

dVc/dt=I/C

**For an ideal op-amp, SR = ∞ **

** For IC LM 741, SR = 0.5 V/ µs**

** For LF 356, SR = 12 V/ µs**

**Frequency Response :**

Gain of an op-amp is basically a complex number that is a function of frequency. Therefore at a given frequency the gain will have a specific magnitude as well as a phase angle i.e. variation in operating frequency will cause variation in gain magnitude and its phase angle. The manner in which the gain of the op-amp responds to different frequencies is called frequency response. A graph of the magnitude of gain versus frequency is called frequency response plot.

The changes in gain & phase according to frequency variation are basically due to the internal capacitances. These capacitances are due to the physical characteristics of semiconductor devices (BJTs & FETs) and the internal construction of op-amp.

The open loop voltage as a function of frequency is shown below

AOL=A/(1+j(f/fo ) )

Where, AOL is the Open loop gain as a function of frequency

A is the the Gain of op-amp at 0 Hz (DC)

f is the Operating frequency (Hz)

f0 is Break over frequency of op-amp (Hz)

The open loop gain magnitude and phase angle is

|AOL |=A/√(1+(f/fo )^2 )

ϕ=-tan^(-1)(f/fo )

The open loop gain AOL (dB) is approximately constant from 0 Hz to the break-over frequency f0. When the input signal frequency f is equal to the break frequency f0, the gain AOL (dB) is 3 dB down from its value at 0 Hz. For this reason the break frequency is sometimes called the -3 dB frequency. It is also known as the corner frequency. The open loop gain is approximately constant up to the break frequency f0, but thereafter it decreases 20dB each time there is a tenfold increase (one decade) in frequency i.e. the gain rolls off at the rate of 20 dB/decade. It can also be stated that the gain rolls off at the rate of 6dB/octave, where octave represents a twofold increase in frequency. Thus wecan describe the roll off rate as either -6dB/octave or -20dB/decade. Finally at some specific value of input frequency, the open loop gain is zero. This specific frequency is called the unity gain bandwidth. Other equivalent terms for it are gain-bandwidth product, closed loop bandwidth, small-signal bandwidth and unity gain crossover frequency.

**For an ideal op-amp, UGB = ∞**

** For IC LM 741, UGB = 1 MHz**

** For IC LF 356, UGB = 5 MHz**

**Input Offset Voltage (Vio) :**

When both the inputs of an op-amp are at ground potential, ideally the output voltage should be zero; but practically some nonzero voltage is present at output terminals. This small voltage is called as output offset voltage (Voo). The output offset voltage Voo is caused by mismatching between two input terminals. Input offset voltage (Vio) is the voltage that is applied between two input terminals in order to make the output offset voltage zero. It is impossible to predict the polarity of the input offset voltage since it is dependent on mismatching between the two input terminals.

**For an ideal op-amp, Vio= 0 V**

** For IC LM 741, Vio = 6 mV**

** For IC LF 356, Vio = 3 mV**

Input Bias Current (IB) :

An input bias current IB is defined as the average of the two input currents I1& I2.

I_B=|(I_1+I_2)/2|

Where I1 is current flowing through Non-inverting terminal. and I2 is the current flowing through inverting terminal.

**For an ideal op-amp, IB = 0 A**

** For IC LM 741, IB = 500 nA**

** For IC LF 356, IB= 20 nA**

Input Offset Current (Iio) :

In op-amp the two input currents are not equal because of the internal imbalances in the op-amp’s circuitry. The input offset voltage is used as an indicator of the degree of mismatching between the two currents.

Mathematically it is defined as the algebraic difference between two input bias currents I1& I2 as

Iio=|I1-I2 |

**For an ideal op-amp, Iio = 0 A**

**For IC LM 741, Iio = 200 nA**

**For IC OP-07, Iio = 3 nA**

Op-Amp Quiz