__OPERATIONAL AMPLIFIERS(OP-AMP)__

**OP-AMP:**An OP-AMP is a direct coupled high gain amplifier usually consisting of one or more differential amplifier.

If a signal is applied at the inverting terminal then the O/P will be out of phase. /180^{* }phase angle.**Specification of ideal (OP-AMP)**

1) I/P Resistance R_{i}= ∞

2)O/P Resistance R_{o }= 0

3)Voltage Gain AV = ∞

4)Band Width BW = ∞

5)Common Mode Rejection Ratio (CMRR) = ∞

6)Slew Rate = ∞

7)Offset Voltage = 0

8)Offset Current = 0

** 1) Input Stage: **This is the double-ended input and double-ended output differential amplifier having large CMRR. One input is the input is the non-inverting input V_{1} and the other is the inverting input V_{2}. It produces most of the voltage gain of the OP-AMP.

** 2)Intermediate Stage: **This is the double-ended input and single-ended output differential amplifier. It is driven by the output of the stage.

**3) Emitter Follower:** The emitter follower is driven by the single-ended output of the second stage. The input resistance of this stage is very high and output resistance very low. Its voltage gain is little less than 1; it is almost unity, and this stag does not produce any phase shift between input and output voltage or current.

**4) Level Shifter:** Because of the direct coupling the dc voltage at the output of the intermediate stage and the emitter follower when no signal is applied is well above the ground potential.

**5) Output Stage:** This is the last stage of an OP-AMP. It is usually a class-B push-pull complementary symmetry power amplifier. This stage increase the output voltage and also increase the current because of low output resistance.

**Ideal OP-AMP:**The ideal OP-AMP has the following characteristics.

1. Its open loop voltage gain in infinite i.e., A= -∞

2. It have infinite input resistance, i.e., R_{i}= ∞. Therefore, signal from voltage source having any internal resistance can be applied, to the op-amp and There is no loading of the preceding stage.

3.It has zero output resistance, i.e., R_{0}= 0. Therefore, its output can be used as input to a number of other devices.

4. It has zero input offset current, i.e., I_{B1}̴ I_{B2}= 0

5. It has infinite slew rate. It means that its output voltage changes simultaneously with changes in the input voltage.

**Parameter OP-AMP: **Practical op-amp fall far short of the op-amp. So we have to consider various parameter that affect their performance. The most important of these are defined in the section.

1) **Input Offset Voltage V _{io}: **For an ideal op-amp when both voltage are zero, the ouput voltage will be zero, i.e., When V

_{1}= V

_{2 }= 0, then V0 = 0. But for a practical op amp.

The input offset voltage for an op-amp is equal to the difference in the values of V_{BE} of the input transistors. Thus V_{io}= V_{BE1 }̴ v_{BE2}

2) **Input Bias Current I _{B}: **Even when the input voltages V

_{1}and V

_{2}of an op-amp are zero, the two dc base current I

_{B1 }and I

_{B2}are never equal because the values of β of the two input transistor are usually different.

3) **Input Offset Current I _{io}: **The input offset current is the difference between the current I

_{B1}and I

_{B2}that flow into the non inverting and inverting input terminal of a balanced op-amp, i.e., when the output voltage is zero. Thus I

_{io}= I

**I**

_{B1}_{B2}

4)

**Open Loop Voltage Gain A**: This is the ratio of the output voltage to the difference of the voltage applied directly to the two input terminal of the top op-amp.

5) **Input Impedance, Z _{i: }**This is the between the inverting and non inverting input terminals, and is usually expressed in terms of resistance only. So it is also denoted by R

_{i}. For the op-amp 741 C the input impedance I about 2 M .

6)

**Output Impedance,Z**This is the impedance between the output terminal and ground, and is usually expressed in terms of resistance only. So it is also denoted by R

_{0}:_{0}. For the op amp 741 C the output impedance is 75Ω.

7)

**Short-**

**Circuit Output Current:**This is the max. current which the op-amp can supply if its output terminal is shorted to ground.

8)

**Supply Voltage Range, V**: Op-amps are usually operated with two dc supplies. The supply voltage must be within max. and min. limits. If the supply voltage are too high the op-amp would be damaged and if they are too low the op-amp will not operate properly.

_{s}9)

**Input Voltage Range, V**If the same voltage is applied to both the input terminals, the op-amp is said to be in the common –mode configuration, and the voltage is called the common-mode voltage, V

_{1(max)}:_{CM}.

10)

**Output Voltage Swing or Ac Output Compliance PP:**The output voltage swing or the ac output compliance, PP is the max. undistorted peak-to-peak output voltage that an op-amp can produce for sine wave point input voltage.

11)

**Power Supply Rejection Ratio, PSRR:**This is ratio of the change in the input offset voltage to the corresponding change in the voltage of one power supply, when the voltage of all remaining power supply are constant.

12)

**Common-Mode Rejection Ratio:**For an op-amp the common-mode rejection ratio(CMRR) is defined as the ratio of the magnitude of the differential-mode voltage gain A

_{d}to the magnitude of the common-mode voltage gain A

_{CM}.

13) **Open-Loop Cut-off Frequency, f _{OL} and Unity Gain Frequency: **For small input signal the frequency response of the open-loop op-amp741 C. The frequency response curve shows that the open-loop voltage gain |A

_{OL}| in the frequency region from 1Hz to about 5Hz is constant approx. equal to 100dB.

14) **Slew Rate, S: **The max. rate of change of output voltage with respect to time, produced by an op-amp, when the voltage gain is unity, is called it slew rate S.

**Inverting Configuration:**It is the configuration in which the feedback resistor R_{2}is connected from the output terminal of the op-amp back to the inverting or negative input terminal. This type of feedback is known as negative feedback. This configuration is studied in this section. An op-amp in inverting configuration is also known as inverting amplifier.

**Non-inverting Configuration**: It is the configuration in which the feedback resistor R_{2}is connected from the output terminal of the op-amp back to the non-inverting or positive input terminal. This type of feedback is known as positive feedback. An op-amp in non-inverting configuration is known as non-inverting amplifier, which will studied in next section.**Inverter:**In the basic inverting amplifier, if the ratio R_{f}/R_{1}= k, where K is real constant, then the closed loop gain A_{CL}= -K. The circuit thus could be used to multiply by a constant, then the R_{1}and selected as precision resistor. For R_{f}= R_{1}, A_{CL}= -1 and the circuit is called inverter, i.e., the output is 180^{0}out of phase with respect to input through the magnitude are same.

**Adder:**Op-amp may be used to design a circuit whose output is the same of serval input signals. Such a circuit is called summing amplifier or a adder.I

_{a}+I_{b}+I_{c}=I

V_{a}-0/R_{a}+V_{b}/R_{b}+V_{c}= -V_{0}/R_{f }

V_{a}= V_{b}= V_{c}= V_{i }

R_{a}= R_{b}= R_{c}=R

V_{i}/R = V_{0}/ R_{f }

R_{f}/-R = V_{o}/ V_{i }

V_{0}/V_{a}+V_{b}+V_{c}= R_{f}/ R_{a}+R_{b}+R_{c}

**Subtractor:**A basic differential amplifier can be used as subtractor. If all resistor in value, then the output voltage can be derived by using superposition principle. To find the output V_{01 }due to V_{1 }alone, make V_{2}=0.V

_{01}=V_{1}/2[1+R/R]

V_{02}= -V_{2}

V_{0}= V_{01}+V_{02}= V_{1}-V_{2}

**Differentiator:**The differentiator circuit can be obtained by inter-changing the resistor and capacitor of the integrator circuit. Its function is to provide an output voltage which is proportional to the rate of the change of the input voltage.I

_{c}= I_{R}

I_{c}= C d_{vc}/dt

I_{c}= C d_{vc}/d_{t}

Apply KCL

C d(V_{s}-0)/dt = 0-V_{0}/R

I_{c}= I_{R}

V_{0}= -R_{c}d_{vc}/d_{t}**Integrator:**The function of an integrator is to provide an output voltage which is proportional to the integral of the input voltage. In this circuit instead of feedback resistor, capacitor is placed in the feedback.I

_{C}= I_{R}

I_{R}= V_{S}-0/R = V_{S}/R

V_{S}/R = C d/dt (0-V_{0})

∫V_{S}dt = R_{C }∫dt (-V_{0})

∫V_{S}dt/R_{C}= -V_{0}**Voltage Follower:**The circuit arrangement for a voltage followers. The feedback resistance R_{f}= 0 and input resistance R_{1 }= ∞. An important application of non-inverting configuration which uses the property of high impedence. This circuit is useful as buffer amplifier because it allow the input voltage (V_{in}) to be transformer as output voltage V_{0}while at the same time preventing the load resistance from loading down the input source.

**Voltage to Current ( V To I) Converter:**Sometimes, it may be required to convert an input voltage into an output current. The circuit for the required operation can be designed using op-amp, and is called voltage to current converter.**V to I Converter With Floating Load**

When the load resistor R_{L}is not connected to ground, the load is said to be floating load. In V-I converter. The load resistor is not connected to ground.V

_{id}≅ 0V

V_{1}= V_{in}

V_{1}= i_{1}R_{i}

Applying KCL at node V_{1},

we get

i_{out}= i_{1}+ I_{B}

Since I_{B}= 0

i_{out}= i_{1}= V_{in}/R_{i}**Equation shows, that output current i**_{out}is set resistor R_{i}.**Current to Voltage (I To V) Converter:**Let us consider the dial voltage gain equation of inverting VCVS and related to the circuit.**Assuming ideal condition, we get**

V_{out}/V_{s}= R_{f}/R_{s}

Where

V_{s }= I_{s}R_{s}

is the source voltage and R_{s}is source resistance

V_{out}/R_{s}I_{s }= R_{f}/R_{s }

V_{out}= -I_{s}R_{f}_{ }Thus, if the replace Vs and Rs combination in an inverting op-amp by a current source, the output voltage becomes proportional to the input current I

_{s }. In other words, a converts input current into proportional output voltage. This current to voltage converter make an excellent current measuring instrument since it is an ammeter with zero voltage across the meter, I to V converter is also known as transresistance amplifier.**Current Amplifier:**This op-amp can be employed for current amplification as well, based on op-amp configuration the current amplifier are two types:

1) Inverting Current amplifier

2) Non-inverting amplifier

The current amplifier are used in remote sensing instrumentation and voltage to frequency converter input signal conditioning.**Inverting Current Amplifier:**Assuming ideal op-amp, no current enter into the op-amp. So I_{in}current flows through feedback resistor R_{f}.I

_{in}= V_{2}-V_{out}/R_{f}

Again as no current enters into the op-amp.

∴ Current through resistor R_{1}will be the load current

I_{L}= V_{out}– V_{1}/R_{1}With V_{id}= 0.

V1 = V2.

Hence, we get I_{in}R_{f}= -I_{L}R_{1}

I_{L}= - R_{f}/R_{1}I_{in}

Or

The negative sign shows that the circuit is an inverting current amplifier. Here if R

_{f}= R_{!}then I_{L }= -I_{m}and the circuit is called as current reverser.

**Non – Inverting Current Amplifier:**The current amplifier based on non-inverting configuration of op-amp. Assuming ideal op-amp, no current enters into the op-amp. Hence, input current I_{in}flows through R_{2},where

I_{in}= V_{1}- V_{x}/ R_{2}

With V_{i}= V_{2}= V_{out},

we get I_{in}= V_{out}– V_{x}/ R_{2}

The current flows through resistor R_{1}can be obtained as

I_{R1}= V_{out}– V_{x}/ R_{1}

We get,

I_{R1}= R_{2}/ R_{1}I_{in }

By Applying KCL at node x,

we get

I_{L}= I_{in}+ I_{R1}= I_{in}+ R_{2}/ R_{1}I_{in}

I_{L}= {1+ R_{2}/R_{1}}I_{in}**Log Amplifier:**The fundamental log-amp circuit where a grounded base transistor is placed in the feedback path. Since the collector is held at virtual ground and the base is also grounded, the transistor’s voltage-current relationship becomes that of a diode.

I_{D}= I_{e}V_{o}/ ɳV_{T}

For i/p

I = V_{i}– 0 / R .....(1)

I = V_{i}/ R

For I_{D}= I_{oe}- V_{o}/ ɳV_{T .......}(2)

Because

V_{D}= 0 – V_{0}

Equation (1) and (2)

I = I_{D}V_{in}/ R = I_{oe}–V_{o}/ ɳV_{T}

e- V_{o}/ ɳV_{T}= V_{i}/ RI_{o}

Taking log both side

Log e- V_{o}/ ɳV_{T}= log V_{i}/ RI_{o}

–V_{o}/ ɳV_{T}= log V_{i}/ RI_{o}**V**_{o}= –V_{o}/ ɳV_{T}log V_{i}/RI_{o}

Or**V**_{o}= - ɳV_{T}log V_{i}–log RI_{o}*I*_{o}= reverse saturation current so I_{o}<< R then**V**_{o}= - ɳV_{T}log V_{i}/ RI_{o}**V**_{o}= -log V_{i}**Anti-Log Amplifier:**The input V_{i}for the antilog-amp is fed into the temperature compensating voltage divider R_{2}and R_{TC}and then to the bas of Q_{2}. The output V_{o}of the antilog amp is fed back to the inverting input of A_{1}through the resistor R_{1}. The base to emitter voltage of transistor Q_{1}and Q_{2}**.**I

_{D}= I

I_{oe}– V_{B}/ ɳV_{T}= 0-V_{o }/ R

I_{oe}V_{ia}– 0 / ɳV_{T}= -V_{o}/ R**V**_{o}= -R I_{oe}V_{in}/ ɳV_{T}

**Precision Rectifier:**Rectifier normally used for converting ac to dc work in the range of voltage something like 5v to 50v. In such cases the drop across the diode does not become significant. However, there are applications where very small voltage of the order of 100 mV has to rectified. Here voltage drop across the diode ( 0.7V) cannot be ignored. There are two types of Precision rectifier:

1) Super Diode Half-wave Rectifier

2) Precision Full-wave Rectifier.

1)**Super diode Rectifier:**Super diode is nothing but a diode having ideal characteristics.(V

_{i}– V_{o})A = -V_{A}

V_{A}+ 0.7 v + V_{o}= 0

(V_{0}– V_{i})A + 0.7 v + V_{o}= 0

V_{o}(1+ A) = V_{i}A - 0.7 V = 0

Vo = AV_{i}/ 1+ A – 0.7 / 1+A

V_{o}= V_{i}

Is this circuit of the precision rectifier also. The circuit consists of a diode in the negative feedback path of the op-amp, with R_{L}as the rectified load. [ As V_{i}start increasing in the positive half cycle, the output V_{A}of the op-amp., becomes increasing positively and hence, diode is forward biased and start conducting. As A 10^{4}, A/(1+A) = 1 and 0.7 V/(1+A)=0. Hence, V_{o}= V_{i}. Thus in the positive half cycle, the circuit works as a voltage follower and output is exactly the same as the input. In the negative half cycle, V_{i}, V_{o}, V_{A}, V become negative and the diode does not conduct and hence, no voltage is developed across code R_{L}.

**Precision Full-wave Rectifier:**The full-wave rectifier also called absolute value circuit. for +ve half cycle input voltage, i.e., V_{i}>0, diode D_{1}conducts as V_{A}become –ve and diode D_{2}is reverse biased.

V_{o}= (-2/3)V_{i}(1+1/2) = -V_{i }_{ }_{OP-Amp Comparator: Basic comparator circuit is the one that makes a comparison between some fixed voltage and a reference voltage.The op-amp application as of a comparator (non-inverting) as the input voltage is being fed on to the non-inverting terminals.When Vin < Vref , the output voltage vo is at a (-Vsat ≅ - VEE) as the voltage at –ve input is higher than that at +ve input.}_{}- On the other hand, When V
_{in}> V_{ref }, the +ve input V_{in}> V_{ref}, the +ve input becomes positive with respect to-ve input and V_{o}goes to +v_{sat}( V_{CC}). hence in the way V_{o}changes from one saturation level to another.

Comparator is in way a type of analog-digital converter. It is also called as a voltage level detector. **Analog Multiplier:**With the help log & anti log amplifier we can multiply & divide two analog voltage.

K_{1}log V_{1}+ K_{1}log V_{2}

K_{1}K_{2}log V_{1}V_{2}

K_{1}= K_{2}= K

K(logV_{1}+ log V_{2})

K log V_{1}V_{2}**Schmitt Trigger Using OP-AMP:**It’s a comparator with +ve feedback which converts any wave form into rectangular or wave. In Schmitt trigger varying T_{on}and T_{off}making a square gate. If feedback is +ve in op-amp then o/p is +V_{sat}or –V_{sat}. if –ve terminal is at higher, o/p is –ve & if +ve terminal is at higher, then o/p is+ve initially assume that V o/p = +V_{sat }_{}_{Vo = +Vsat V1 = R2/R1+R2 * (+Vsat)V1 = VUTPUTP- upper trigger potentialVin < UTPVo = +VsatVin ≥ VUTPVo = -VsatFrom here we get that Vo changes for +Vsat to –Vsat.V1 = VLTP LTP- low trigger potentialVin ≥ VLTP Vo = -VsatVin < VLTPVo = +VsatFrom here we get that Vo change for – Vsat to + Vsat and again V1 changes for VLTP to VUTP and this process repeat. }**Astable Mutlivibrator:**Initially assume that V_{o}= +V_{sat }_{}_{V1 = R2/R1+R2 * +VsatV1 = VUTPThen, capacitor starts charging through ‘R’ toward +Vsat when V2 = Vc ≥ VUTP then Vo changes from +Vsat to –VsatBecause Vc>V1After that capacitor start discharging towards –Vsat through ‘R’ thenV1 = R/(R+R2) * -VsatV1 = VLTPV2 = Vo < VLTPVo/p changes from –Vsat to +Vsat V1 changes from VLTP to VUTP and this process repeat. }_{ }**Mono Stable Multivibrator:**Monostable multivibrator has one stable state and the order is quasi stable state. The circuit is useful for generating single output pulse of adjustable time duration in response to a triggering signal. The width of the output pulse depends only on external components connected to the op-amp. The circuit is a modified form of the stable multivibrator. A diode D_{1}clamps the capacitor voltage to 0.7v when the output is at +V_{sat}. A negative going pulse signal of magnitude V_{1}passing through the differentiator R_{4}C_{4 }and diode D_{2}produces a negative going triggering impulse and is applied to the (+) input terminal.**Triangular Wave Generator:**If we integrate square wave then we will get triangular wave form. A triangular wave can be simply obtained by integrating square wave. It is obvious that the frequency of the square wave and triangular wave is the same. Although the amplitude of the square wave is constant at V_{sat}, the amplitude of the triangular wave will decrease as the frequency increases. This is because the reactance of the capacitor C_{2}in the feedback circuit decrease at high frequencies. A resistance R_{4}is connected across C_{2}to avoid the saturation problem at low frequencies as in the cases of practical integrator.

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