Ideal-Practical Opamp

Characteritic parameters

Differential Amplifier

Virtual Short in Opamp

Instrumentation Amplifier

Sqare Wave Generator

Schmitt trigger

741 Opamp PIN Diagram

Voltage follower- sample and hold

Lag and Lead Compensators

Bridge amplifier

Precision diode- Halfwave Rectifier

Peak and Zero Crossing Detector

Integrator-Differentiator

Log and Anti-Log Amplifiers

Inverting- Non inverting Amplifiers

Oscillators

**Definition**

Astable Multivibrator is also called as Free running multivibrator or relaxation oscillator with no stable states. It is a square wave generator and has two unstable states.It oscillates back and forth between these two states when the circuit is given power supply.

**Circuit Diagram**

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**Design equations**

The Time period of Square wave

** T = 2*R*C*ln((1+β)/(1-β))**

Assume R_{1}=R_{2} then **T= R*C*ln(3)**, in which the values of** R** and **C** can have any combination based on availability of capacitor and resistor but should satisfy the time period equation.

**Circuit analysis**

The output** **of opamp is **+V _{cc}**if

**V**

_{2}>> V_{1}**and is**

**–V**

_{cc}**if**

**V**

_{2}<< V_{1}**.**Assume that the output initially is at positive saturation value of

**+V**. By voltage divider rule the voltage at non inverting terminal of opamp is

_{cc}**Vcc*R**.

_{1}/(R_{2}+R_{1})**The capacitor starts charging through R with time constant R*C and the voltage across capacitor is given by**

**V**. When the voltage across the capacitor is just more than

_{c}= V_{cc}*(1-exp(-R*C*t))

**V**,

_{cc}*R_{1}/(R_{2}+R_{1})**at that instant the output of opamp changes to**

**–V**.Now the

_{cc }**V**,the capacitor has to discharge through R till it reaches to a value less than

_{c}= -V_{cc}*R_{1}/(R_{2}+R_{1})**-V**. At that instant when

_{cc}* R_{1}/(R_{2}+R_{1})**V**, output will be

_{1}<< -V_{cc}* R_{1}/(R_{2}+R_{1})**+V**. During the charging and discharging time voltage across the capacitor will be

_{cc}**V**. Hence the voltage across capacitor switches between

_{c}=-V_{cc}*exp(-R*C*t))**-V**and

_{cc}* R_{1}/(R_{2}+R_{1})**+V**and output switches between

_{cc}* R_{1}/(R_{2}+R_{1})**+V**and

_{cc}**-V**. The voltage acroos the capacitor during charging time is given by V

_{cc}_{c}= V

_{cc}*(1-(1+β)exp(-t/(R*C)) where

**β = R1/(R2+R1)**.

Let us assume that the voltage across capacitor at t= 0 s is equal to -V_{cc.}.At = T/2 _{ }output transits from **-V _{cc}** to

**+V**.

_{cc}Hence at t=T/2 **Vc=β*Vcc, **substituting in V_{c} = V_{cc}*(1-(1+β)exp(-t/(R*C)) we get

**β*V _{cc}= V_{cc}*(1-(1+β)exp(-T/(2*R*C)))**

**T = 2*R*C*ln((1+β)/(1-β))**

Hence the frequency of oscillation of square wave is f=1/T.

**Remarks**

This circuit can be used for generating square waves with frequencies of the Kilo hertz order. The slew rate of opamp poses a limitation in generating still higher frequency square waves.