Introduction to Operational Amplifiers

 

 

It is complete amplifier  which is configurable  using external components for desired applications.  It was originally designed  for various type of mathematical operations.   Circuits can be built to perform Multiplication. Division. Addition subtraction, Logarithmic  manipulations, Integration,  Differentiation  etc.  It can be used to perform signal amplification, attenuation, Oscillator, Filters, Comparator, Signal generator  and many other applications.

It is very easy to tailor this amplifier for various application.   The Symbol and  a picture of very popular  741  Op-Amp is given below.

Fig. 1

 

Fig. 2

 

 

The ideal Op-Amp has the following Characteristics.

            Open loop gain A_V  is infinite  i.e. ,   A_{V  =  ∞}

          Its input Resistance is  Infinite.

            Out put resistance is zero.

            It has an infinite bandwidth

Fig. 3

 

 

These  characteristics are nor achievable practically.  In reality these properties  set a benchmark  for the evolution of high performance Op-Amps.

            Infinite  input resistance mean that input current flow is very  minute, almost zero.  This property  shows that Op-Amp is a Voltage-Controlled device.

            When  output Impedance/resistance  is zero,  it  mean that Output Voltage is not dependant on the Load connected at output.

            When we say that its Gain is infinite, it does not mean that a very small input will be amplified to very high voltage at Output.  Maximum value of the output is limited to the Power supply of Op-Amp.     If gain is 10⁶   then 1 μV at input will give 1 V at output.

 

 

 

 

 

 

 

 

 

 

 

 

This figure shows the typical block diagram of an  most common type if Operation Amplifier.  There are two inputs,  Inverting  and Non-Inverting.    There is a single Output.   And  there two inputs for the Positive and Negative power Supplies.

 

            Non Inverting Input:    If  a signal is applied at this input   a  signal of same polarity is produces at the output terminal.

            Inverting Input:    If a signal  is applied at the inverting- input terminal,   a signal  of opposite polarity is produced at the output terminal.   In case of sinusoidal input,  a signal having   phase difference of  180° shifted  will be produced at output terminal.

 

            Out Put:    As this amplifier is a   differential amplifier.  This mean if v1 signal is applied  at the inverting input and v2 is applied at the non-Inverting input, difference of two voltages will be applied at the input of amplifier,     and output will depend upon this difference of voltages,  multiplied by the gain(AV) of the amplifier.    output  vo  =  Av(v2-v1).

 

 

 

 

 

 

 

 

 

Op-Amp Power supply

            Op-amp has two supply inputs.  V+,   V-.    Op-Amp  can be connected to power supplies in either of following ways.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Op-Amp  Parameters

 

            The parameters described below are  very necessary to understand  the basic concepts of the Op-Amp  operation.

           

1. Gain.

As it has been already stated the an ideal Op-Amp has Infinite op-loop differential  gain.  But practical Op-Amps have the Finite Gains.  It can between  25,000 to 3,00,000.  

Gain is expressed and manipulated  in decibels (dB).  If v1  and v2  are the input voltages then  gain in dB  will be:

            Gain(dB)  =  20log₁₀  .

2. Input Resistance

According to specifications  of an ideal Op-Amp,  Input resistance  of the Op-Amp  is  infinitely  high.   But in real practice  it falls in the range  of  250 KΩ  to  40 MΩ,  for the Op-Amps  with input stage made with Bi-Polar Transistors.   For the Op-Amps with  Field Effect Transistors(FET)  input it can be  10¹²Ω.    

3. Output resistance

For an ideal Op-Amp  Output resistance is zero.  Practically it is not possible.  As  discussed earlier,  Op-Amp is a Voltage Amplifier.  Therefore it should have Output resistance as low as possible.  Practical Op-Amp’s Output resistance is of the order of  100Ω.

4. Common Mode Rejection Ratio (CMRR)
5. Output  voltage of an Op-Amp  is proportional to the difference between the  Input voltages applied  to the  inverting and non-inverting inputs.  These input signals are called common mode signals.
6. Ideally when two applied voltages are equal,  the output voltage should be equal to zero. 
7. In the real case if Noise signal  gets applied to both inputs, then  it should not appear at the output. 
8. In practical  such signals are not completely cancelled out.  At it exists at the output as a unwanted noise.
9. So the ability  of cancelling out common mode signals at output is  considered as  an important property of Op-Amp  and  expressed  in term of Common Mode rejection ratio(CMRR).

CMRR  =    = 

                        The Common mode rejection ratio  is also expressed in term of decibels

                                    CMRR  =  20 log₁₀  dB.

                        Op-Amp can have a common mode rejection ratio of  90 dB.

5. Slew Rate

It is the maximum rate of change  at which,  output  voltage is capable of changing.    It is expressed as  V/μs.  As an example  μA 741  Op-Amp  has slew rate of 0.5 μA.

 

 

 

 

 

 

 

 

 

The slew rate is the main hurdle  in the  way of maximum operating  frequency of the Op-Amp.  So slew rate can be used to  determine the maximum operating frequency of OP-Amp.

                       

                                                f_max  =                         

6. Bandwidth

Bandwidth  of an ideal Op-amp is Infinite.  In real case  open loop gain is not constant at all frequencies.  It falls off at higher frequencies,  due to capacitive effect. 

 

 

 

 

 

 

 

 

 

 

 

7. Input Offset Voltage

Ideal Op-Amp should give output voltage  equal to zero, when value of applied voltage to both inputs is zero.   However  practically  it is found that some output voltage does exist for zero input voltage.  It is normally in the range of 10 μV  to 7 mV.     Input offset voltage   is defined as  output voltage for zero input voltage  divided by the open-loop voltage gain of the Op-Amp.

 

8. Input Bias Current

Base Bias currents of the both transistors of input differential amplifier should be equal.  Due to some  manufacturing imperfection there is always some difference between the two currents. These currents must be same for balanced operation of Op-Amp.

9. Input Offset Current

The difference between the Bias currents is  known as input Offset current. It value is 3-20 nA for Op-Amp with bipolar transistor inputs.

           

 

 

Virtual Ground and Summing Point

            Before moving to applications of Op-Amp,  learning about Virtual Point and Summing Point is required.

 

 

 

 

 

 

 

 

 

 

 

 

Input to the Op-amp is V1,  and a feedback from output is being added to the Input at  point A.  This  point is called summing point.

            Input voltage Vi  at the inverting terminal  of  Op-Amp  is made  such a small value that  its value may be assumed as zero.  Point A is at ground level.   So point A is referred as Virtual Ground.  But remember that it is not actual Ground point.

 

 

 

 

 

Inverting Amplifier

 

            A configuration of an inverting amplifier  is shown in the Fig.9,  by using a Op-Amp. 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

In  the figure  Non-Inverting Terminal is grounded.  Input signal Vin  in being applied to inverting input through resistor R1.    Resistor  Rf   feedbacks the output  to the inverting  input of Op-Amp.

Since point A  is the virtual ground so: 

Vin  =  I1 . R1      or       I1  = 

VO   =  - I2 . Rf      or      I2  = -

Practically   Power drawn by the inverting input is zero.   So all input current flows through Rf.  Therefore      I1  =  I2     so         =  -

From above equation   we get,

                                                VO  =-   Vin         also  it can be written as    = -        

But    voltage gain   Av  =      so      Av  = -        

 This equation shows  that  Gain of the Op-Amp can be set / determined by the  dividing the value of R2  by  R1.    The Negative sign shows that output of the inverting amplifier is 180°   out of phase fron the input signal.

 

 

The open loop and closed loop gain.   The open loop voltage gain (A_OL)  of an Op-Amp  is the gain that is measured, when there is no feedback  path between output and input. 

            If a feedback path exists between the output and input, then circuit’s gain is called closed-loop gain (A_CL).

Input Resistance (R_in).    As input resistance of OP-Amp is very high.   In the circuit of Inverting amplifier,  the R₁  is the resistance connected between the input signal  and virtual ground.   So voltage source at input finds the input resistance as  a parallel combination of R₁ and  Input resistance of Op-Amp.    As  input resistance of Op-Amp is very  high  than R₁, so  Input resistance of inverting Op-Amp is,     Rin  =  R₁ .

Output Resistance.    As output resistance of the inverting amplifier  is the parallel combination of  R_f and  output resistance of Op-Amp itself.  Since the O/P resistance of the Op-Amp is very low,  In the Inverter Amplifier  case  it becomes less than O/P resistance.

Common Mode Rejection Ratio.  CMRR in the case of Inverting Amplifier is:   CMRR  = 

                                                        Here        A_CL  is closed loop gain of Inverting Amplifier.

                                                                        A_CM  is the common mode gain of the Op-Amp

 

 

 

Example:    Find the maximum allowable  value of V_in

For the circuit shown.  Assume the gain of Amplifier

  Is 200.

 

Solution:   It is given  that  A_CL =  200,  and V_o  +  8V.

 

                        As   Av  = 

                        So   200 = -  = -

                        So   V_in  =  -    =  - 0.04V  =  -40 mV.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Non-Inverting Amplifier

 

            A configuration of a non - inverting amplifier  is shown in the Fig.10,  by using a Op-Amp. 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

In  the figure,  Input signal Vin  in  applied to non-inverting input of Op-Amp.  Resistor R1     Is connected to Ground. Resistor  R2  is a feedback  resistor between output and inverting  input of Op-Amp.  

The output attempts to do whatever is necessary to make the voltage difference between the inputs zero. The voltage gain of a real op-amp is so high that a fraction of a milli-volt input will swing the output over its full range.    Therefore difference between the  voltages  at the both inputs  is so small that they can be considered equal.

V_in  =  V_i

If  I₁   is the current flowing through R₁ then               I1  =     or     Vin  =  I1 . R1 …….i   

Since  the voltage drop across R₂  is equal to   V_o -  V_in

 So   Current through resistor  R₂    will  be:                 I₂  =          or    I_{2 .} R₂  =  V_O  -  V_in

Therefore   VO   =  Vin  +   I2 . R2       

 

Practically Power drawn by the inverting input is zero.   So I₁   and  I₂  are considered equal as same current passes through  R₁  and R₂. 

Therefore      I1  =  I2     so     replacing I₂  by  I₁  in above equation we get,

                                VO   =  Vin  +   I1 . R2  …………….ii

 

Amplifier  Voltage Gain,  A_V  =        =    

Putting  Values of VO  and  Vin  in the above equation we get

                                        A_V  =                  

Putting the values of V_O  and Vin  we get      

                                                 

Av  =  =    =   

                                Av  =  1  +         This is the equation for the gain of  Non Inverting Amplifier.

Note that the gain of Non-inverting Amplifier is greater than the gain of Inverting Amplifier.

 

Input Resistance.   Note that  input signal is applied directly to the input of Op-Amp.  Therefore input resistance of Non-Inverting Amplifier is very high.

Output Resistance.  Output resistance of Non-Inverting Amplifier is less than  the  output resistance of the Op-Amp itself.

Common Mode Rejection Ratio.     CMMR  = 

 

 

 

Example.    Find the value of close loop gain (A_CL),  Common Mode Rejection ratio,   and maximum Operating frequency of the  non-Inv-Amplifier,   A_CM  = 0.001,  and  slew rate = 0.5V/μs.

 

Solution.    It is given  that   A_CM  =  0.001,  R₁  =  10K,

R₂  =  100K,  R_L  =  10K ,  V_IN  =  1V_PP.

 

Closed-loop gain of N-Inv-Amp  A_CL  =  1  +         

            =  1  +      =  1  +  10  =  11   

 

Common Mode Rejection Ration  CMMR  = 

A_CL  =  11,  and  A_CM  =  0.001

So      CMMR  =    =     =  11,000.

 

We know that  V_IN  =  1V_PP  and    A_CL  =  11   so    V_OUT   =   1 x 11 V_PP  =  11 V_PP 

From V_PP  we can find  V_{P K}  =   5.5

 

And Maximum Frequency  f_MAX  =     =     =   = 14.47 x 10³  Hz.

                                                                                                                               =  14.47 KHz.

Voltage Follower.  

 

            The Non-Inverting Amplifier  is modified

As shown in the Fig.11,  to make a Voltage

Fig. 10

Follower Amplifier.   Notice that output is directly

Connected to the Inverting Input of the Op-Amp.

 

Equation for voltage gain is      Av  =  1  +           

Here  R₁  =  R₂  =  0   so we get  Av  =  1  

 

            It acts as a Buffer Amplifier.   This voltage follower has very high Input Impedance  and veru low  output Impedance.

 

            CMMR  =    =      As closed loop gain (A_CL)  is equal to 1.

 

 

1.      For the Voltage Follower  shown,  find  the value of A_CL,  CMMR,  and  fmax.

A_CM  =  0.001,   A_OL  =  180,000,   Z_IN  =  1M,  Z_OUT  =  80M,   Slew Rate  =  0.5 V/μs,  V_IN  =  6VPP,

 

            As  A_CL  =  1  +   ,  for Voltage follower  R₁  =  R₂  =  0

            So  A_CL  =  1, 

            CMMR  =     =      =  1000.

 

To calculate Maximum Operating Frequency

            V_IN  =  6V_PP,  A_CL  =  1,   

So        V_OUT  =  6 x 1  =  6V_PP

 

Thus   Peak Output voltage  =  3V_PK    and

 

f_MAX  =     =     =   = 26.5 KHz  Hz.

 

 

 

 

 

 

 

Summing Amplifier(Inverting).   

Fig. 11

 

The Summing Amplifier is a very flexible circuit based upon the standard Inverting Operational Amplifier configuration. As its name suggests, the “summing amplifier” can be used for combining the voltage present on multiple inputs into a single output voltage.

 

If  R₁  =  R₂  =  R₃    then   V_O  =  -  (V₁  +  V₂  +  V₃)

 

  (Derivation has not been shown)

 

 

Summing Amplifier(Non-inverting).   

Fig. 12

 

Without showing the derivation  the value of

Output is,

 

V_O    =    (1  +    )(   )  

 

 

 

 

Fig. 13

Without showing the derivation  the value of

Output is,

 

If  R_F  =  R₁,  Then   V_O   =  (V₂  -V₂)

 

 

 

 

 

 

 

 

 

 

 

Differential Amplifier.

 

Fig. 14

Fig. 14  shows the circuit of a Differential Amlifier.

If V1  and V2 is applied at the inputs of the Amplifier

Then Vo will be equal to the difference between  the

Two voltages applied at the inputs.

 

If  R1  =  R3,  and  R2  =  R4  then

 

AV  =          and    V_O  =    (V₂  -  V₁)      

 

 

 

 

Fig. 15

Integrator  Amplifier.

 

Fig. 15  shows the circuit of a Integrator  Amlifier.

It will produce Vo  which will be the Integration of the Vin.

 

Vo  = -  

 

 

Differentiator  Amplifier.

 

Fig. 16

Fig. 16  shows the circuit of a Differentiator  Amlifier.

It will give Vo at output  whill will be differenciation of Vin.

 

Vo  =   -R₁C₁