Practical OP-AMP

Posted By on September 12, 2014


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Ideal Vs Practical or Real Opamp
Applied Electronics Assignment 3

Intro

Op Amp is a short hand term for Operational Amplifier. An operational amplifier is a circuit component that amplifies the difference of two input voltages:

Vo = A (V2 – V1)

Op Amps are usually packaged as an 8-pin integrated circuit.

Operational Amplifier IC Chip
Pin Usage
1 Offset Null
2 Inverted Input
3 Non-Inverted Input
4 -V Supply
5 No use
6 Output
7 +V Supply
8 No use

Op Amp symbol op-amp

  • V+: non-inverting input
  • V: inverting input
  • Vout: output
  • VS+: positive power supply
  • VS−: negative power supply

Op amps amplify AC signal or AC Voltage better than a simple bipolar junction transistor.

Op Amp Functions

Voltage Difference Amplifier

From above

V0 = A (V2 – V1)

Voltage Comparator

V2 > V1 , V0 = +Vss
V2 < V1 , V0 = -Vss
V2 = V1 , V0 = 0

Inverting Amplifier

With one voltage is grounded

If V2 = 0 , V0 = -A V1 . Inverting Amplifier

Non-Inverting Amplifier

With one voltage is grounded

If V1 = 0 , V0 = A V2 . Non-Inverting Amplifier

Linear Configurations

Differential amplifier

Differential amplifier
 V_mathrm{out} = V_2 left( { left( R_mathrm{f} + R_1 right) R_mathrm{g} over left( R_mathrm{g} + R_2 right) R_1} right) - V_1 left( {R_mathrm{f} over R_1} right)
  • Differential Z_mathrm{in} (between the two input pins) = R_1 + R_2

Voltage Difference Amplifier

Whenever R_1 = R_2 and R_mathrm{f} = R_mathrm{g},

 V_mathrm{out} = {R_mathrm{f} over R_1} left( V_2 - V_1 right)

Voltage Difference

When R_1 = R_mathrm{f} and R_2 = R_mathrm{g} (including previous conditions, so that R_1 = R_2 = R_mathrm{f} = R_mathrm{g}):

 V_mathrm{out} =  V_2 - V_1 ,!

Inverting Amplifier

Inverting amplifier
 V_mathrm{out} = - V_mathrm{in} left( {R_f over R_1} right)

Inverting Amplification is dictated by the ratio of the two resistors

Non-Inverting Amplifier

Non-inverting amplifier
 V_mathrm{out} = V_mathrm{in} left( 1 + {R_2 over R_1} right)

Non-Inverting Amplification is dictated by the ratio of the two resistors plus one

Voltage Follower

Voltage follower

From Non-Inverting Amplifier’s formula. If the resistors has the same value of resistance then output voltage is exactly equal to the input voltage

 V_mathrm{out} = V_mathrm{in} !

From Inverting Amplifier’s formula. If the resistors has the same value of resistance then output voltage is exactly equal to the input voltage and inverted

 V_mathrm{out} = - V_mathrm{in} !

Summing amplifier

Summing amplifier
 V_mathrm{out} = - R_mathrm{f} left( { V_1 over  R_1 } + { V_2 over R_2 } + cdots + {V_n over R_n} right)

When R_1 = R_2 = cdots = R_n, and R_mathrm{f} independent

 V_mathrm{out} = - left( {R_mathrm{f} over R_1} right) (V_1 + V_2 + cdots + V_n ) !

When R_1 = R_2 = cdots = R_n = R_mathrm{f}

 V_mathrm{out} = - ( V_1 + V_2 + cdots + V_n ) !

Integrator

Integrating amplifier

Integrates the (inverted) signal over time

 V_mathrm{out} = int_0^t - {V_mathrm{in} over RC} , dt + V_mathrm{initial}

(where V_mathrm{in} and V_mathrm{out} are functions of time, V_mathrm{initial} is the output voltage of the integrator at time t = 0.)

Differentiator

Differentiating amplifier

Differentiates the (inverted) signal over time.

The name “differentiator” should not be confused with the “differential amplifier”, also shown on this page.

V_mathrm{out} = - RC left( {dV_mathrm{in} over dt} right)

(where V_mathrm{in} and V_mathrm{out} are functions of time)

Comparator

Comparator
  •  V_mathrm{out} = left{begin{matrix} V_mathrm{S+} & V_1 > V_2  V_mathrm{S-} & V_1 < V_2 end{matrix}right.

Từ V0 = A (V2 – V1)

  • Vo = 0 khi V2 = V1
  • Vo > 0 khi V2 > V1
Vo = Vss
  • Vo < 0 khi V2 < V1
Vo = V-ss

When two input voltages equal. The output voltage is zero . When the two input voltages different and if one is greater than or less than the other

  1. Vo = Vss khi V2 > V1
  2. Vo = V-ss khi V2 < V1

Instrumentation amplifier

Instrumentation amplifier

Combines very high input impedance, high common-mode rejection, low DC offset, and other properties used in making very accurate, low-noise measurements

  • Is made by adding a inverting buffer to each input of the differential amplifier to increase the input impedance.

Schmitt trigger

Schmitt trigger

A comparator with hysteresis

Hysteresis from frac{-R_1}{R_2}V_{sat} to frac{R_1}{R_2}V_{sat}.

Gyrator

Inductance gyrator

A gyrator can transform impedances. Here a capacitor is changed into an inductor.

 L = R_mathrm{L} R C

Zero level detector

Voltage divider reference

  • Zener sets reference voltage

Negative impedance converter (NIC)

Negative impedance converter

Creates a resistor having a negative value for any signal generator

  • In this case, the ratio between the input voltage and the input current (thus the input resistance) is given by:
R_mathrm{in} = - R_3 frac{R_1}{R_2}

Non-linear configurations

Rectifier

Super diode

Behaves like an ideal diode for the load, which is here represented by a generic resistor R_mathrm{L}.

  • This basic configuration has some limitations. For more information and to know the configuration that is actually used, see the main article.

Peak detector

Peak detector

When the switch is closed, the output goes to zero volts. When the switch is opened for a certain time interval, the capacitor will charge to the maximum input voltage attained during that time interval.

The charging time of the capacitor must be much shorter than the period of the highest appreciable frequency component of the input voltage.

Logarithmic output

Logarithmic configuration
  • The relationship between the input voltage v_mathrm{in} and the output voltage v_mathrm{out} is given by:
v_mathrm{out} = -V_{gamma} ln left( frac{v_mathrm{in}}{I_mathrm{S} cdot R} right)

where I_mathrm{S} is the saturation current.

  • If the operational amplifier is considered ideal, the negative pin is virtually grounded, so the current flowing into the resistor from the source (and thus through the diode to the output, since the op-amp inputs draw no current) is:
frac{v_mathrm{in}}{R} = I_mathrm{R} = I_mathrm{D}

where I_mathrm{D} is the current through the diode. As known, the relationship between the current and the voltage for a diode is:

I_mathrm{D} = I_mathrm{S} left( e^{frac{V_mathrm{D}}{V_{gamma}}} - 1 right)

This, when the voltage is greater than zero, can be approximated by:

I_mathrm{D} simeq I_mathrm{S} e^{V_mathrm{D} over V_{gamma}}

Putting these two formulae together and considering that the output voltage V_mathrm{out} is the inverse of the voltage across the diode V_mathrm{D}, the relationship is proven.

Note that this implementation does not consider temperature stability and other non-ideal effects.

Exponential output

Exponential configuration
  • The relationship between the input voltage v_mathrm{in} and the output voltage v_mathrm{out} is given by:
v_mathrm{out} = - R I_mathrm{S} e^{v_mathrm{in} over V_{gamma}}

where I_mathrm{S} is the saturation current.

  • Considering the operational amplifier ideal, then the negative pin is virtually grounded, so the current through the diode is given by:
I_mathrm{D} = I_mathrm{S} left( e^{frac{V_mathrm{D}}{V_{gamma}}} - 1 right)

when the voltage is greater than zero, it can be approximated by:

I_mathrm{D} simeq I_mathrm{S} e^{V_mathrm{D} over V_{gamma}}

The output voltage is given by:

v_mathrm{out} = -R I_mathrm{D},
Ideal Vs Practical or Real Opamp
Applied Electronics Assignment 3

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Posted by Akash Kurup

Founder and C.E.O, World4Engineers Educationist and Entrepreneur by passion. Orator and blogger by hobby

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