Draw the inverting and non inverting amplifier circuits of an OP-AMP in closed loop configuration. Obtain the expressions for the closed loop gain in these circuits.

Inverting Amplifier Circuit

An inverting amplifier is a configuration where the input signal is applied to the inverting (-) terminal of the operational amplifier (op-amp). The non-inverting (+) terminal is usually connected to ground. Here is the circuit diagram and steps to derive the closed-loop gain:

      +Vcc
       |
       |
       \
       /  Rf
       \ 
       / 
       |
       +----- Vo (Output)
       |
  ----|-\   
      |  >---- 
  ----|-/      
       |
       |      Ri
       +------/\/\/\----- Vin (Input)
       |
      GND

Step 1: Identify the nodes and components.

• Vin is the input voltage.
• Vo is the output voltage.
• Ri is the input resistor.
• Rf is the feedback resistor.
• V- is the voltage at the inverting terminal.
• V+ is the voltage at the non-inverting terminal, which is 0V (grounded).

Step 2: Apply Kirchhoff's Current Law (KCL) at the inverting terminal. Since the input impedance of the op-amp is very high, we can assume that the current into the inverting terminal is negligible. Therefore, the current through Ri is equal to the current through Rf.

Let's denote the current through Ri as Ii and the current through Rf as If. Since Ii = If, we can write:

[ Ii = \frac{Vin - V-}{Ri} ] [ If = \frac{V- - Vo}{Rf} ]

Step 3: Since the op-amp is in a closed-loop configuration, we can assume that the voltage at the inverting terminal is virtually the same as the non-inverting terminal (V- ≈ V+ = 0V).

[ Ii = \frac{Vin - 0}{Ri} ] [ If = \frac{0 - Vo}{Rf} ]

Step 4: Equate the currents and solve for Vo/Vin.

[ \frac{Vin}{Ri} = \frac{-Vo}{Rf} ] [ Vo = -\left(\frac{Rf}{Ri}\right) Vin ]

Closed-loop gain for the inverting amplifier:

[ A_{v} = \frac{Vo}{Vin} = -\frac{Rf}{Ri} ]

Non-Inverting Amplifier Circuit

A non-inverting amplifier is a configuration where the input signal is applied to the non-inverting (+) terminal of the op-amp. The inverting (-) terminal is connected to the output through the feedback resistor. Here is the circuit diagram and steps to derive the closed-loop gain:

      +Vcc
       |
       |
       \
       /  Rf
       \ 
       / 
       |
       +----- Vo (Output)
       |
  ----|+/
      |  >---- 
  ----|-\
       |
       |      Ri
       +------/\/\/\----- V- (Feedback)
       |
      GND
       |
       +------ Vin (Input)
       |
      GND

Step 1: Identify the nodes and components.

• Vin is the input voltage.
• Vo is the output voltage.
• Ri is the input resistor.
• Rf is the feedback resistor.
• V+ is the voltage at the non-inverting terminal.
• V- is the voltage at the inverting terminal.

Step 2: Apply Kirchhoff's Voltage Law (KVL) to the input loop. Since V+ is connected to Vin, we have V+ = Vin.

Step 3: Apply KCL at the inverting terminal. The current through Rf is the same as the current through Ri since the current into the op-amp's inverting terminal is negligible.

[ If = \frac{Vo - V-}{Rf} ] [ Ii = \frac{V-}{Ri} ]

Step 4: Since the op-amp is in a closed-loop configuration, the voltage at the inverting terminal is virtually the same as the non-inverting terminal (V- ≈ V+ = Vin).

[ If = \frac{Vo - Vin}{Rf} ] [ Ii = \frac{Vin}{Ri} ]

Step 5: Equate the currents and solve for Vo/Vin.

[ \frac{Vo - Vin}{Rf} = \frac{Vin}{Ri} ] [ Vo = Vin + \left(\frac{Rf}{Ri}\right) Vin ] [ Vo = Vin \left(1 + \frac{Rf}{Ri}\right) ]

Closed-loop gain for the non-inverting amplifier:

[ A_{v} = \frac{Vo}{Vin} = 1 + \frac{Rf}{Ri} ]

Summary Table

Parameter	Inverting Amplifier	Non-Inverting Amplifier
Input Terminal	Inverting (-)	Non-Inverting (+)
Feedback Connection	Between output and inverting input	Between output and inverting input
Input Resistance	Ri	Very high (ideally infinite)
Voltage at Inverting Terminal	Virtually 0V (ground)	Same as input voltage (Vin)
Closed-loop Gain (Av)	-Rf/Ri	1 + Rf/Ri
Phase Shift	180 degrees	0 degrees

Examples

Inverting Amplifier Example:

• Let Ri = 10kΩ and Rf = 100kΩ.
• Closed-loop gain: Av = -Rf/Ri = -100kΩ/10kΩ = -10.

Non-Inverting Amplifier Example:

• Let Ri = 10kΩ and Rf = 100kΩ.
• Closed-loop gain: Av = 1 + Rf/Ri = 1 + 100kΩ/10kΩ = 11.