For the networks shown below, O/P and I/P are matched with characteristic impedance.
Also, if a(alpha) is the ratio of output to input voltage, find the expression for R1 and R2 for
both the networks.
Answers
Answer:
SORRY
Explanation:
Answer:
Operational Amplifiers
Introduction
The operational amplifier (op-amp) is a voltage controlled voltage source with very high
gain. It is a five terminal four port active element. The symbol of the op-amp with the
associated terminals and ports is shown on Figure 1(a) and (b).
Positive
Vo
Vn
Vp
Ip
In
Io
VEE
Vo
Vp
Vn
VCC
VEE
inverting
input
non-inverting
input
Ic+
Ic-
Output
port
Input
port
power supply
port
Negative
VCC
power supply
port
(a) (b)
Figure 1. Symbol and associated notation of op-amp
The power supply voltages VCC and VEE power the operational amplifier and in general
define the output voltage range of the amplifier. The terminals labeled with the “+” and
the “-” signs are called non-inverting and inverting respectively. The input voltage Vp
and Vn and the output voltage Vo are referenced to ground.
The five terminals of the op-amp form one (complicated) node and if the currents are
defined as shown on Figure 1(a) the KCL requires that
In + Ip + Ic + Ic− + Io = 0 (1.1) +
Therefore for current balance we must include all currents. This is what defines an active
element. If we just consider the signal terminals then there is no relationship between
their currents. In particular,
In + Ip + Io ≠ 0 (1.2)
The equivalent circuit model of an op-amp is shown on Figure 2. The voltage Vi is the
differential input voltage Vi =Vp −Vn . Ri is the input resistance of the device and Ro is
the output resistance. The gain parameter A is called the open loop gain. The open loop configuration of an op-amp is defined as an op-amp circuit without any circuit loops that
connect the output to any of the inputs. inputs.
Ro
Ri
+
_
Vp
Vn
Vi
+
_
+ Vo
AVi
Figure 2. Equivalent circuit model of op-amp device
In the absence of any load at the output, the output voltage is
Vo = AVi = A Vp ( −Vn) (1.3)
Which indicates that the output voltage Vo is a function of the difference between the
input voltages Vp and Vn. For this reason op-amps are difference amplifiers.
For most practical op-amps the open loop DC gain A is extremely high. For example, the
popular 741 has a typical open loop gain A of 200000 Vo/Vi. Some op-amps have open
loop gain values as high as 108 Vo/Vi.
The graph that relates the output voltage to the input voltage is called the voltage transfer
curve and is fundamental in designing and understanding amplifier circuits. The voltage
transfer curve of the op-amp is shown on Figure 3.
Vo
Vi
VEE
VCC
slope=A
Saturation
Saturation
Linear
region
Figure 3. Op-amp voltage transfer characteristics.
the two distinct regions of operation: one around Vi=0V, the linear region where the
output changes linearly with respect to input, and the other at which changes in Vi has
little affect on Vo, the saturation region (non-linear behavior).
Circuits with operational amplifiers can be designed to operate in both of these regions.
In the linear region the slope of the line relating Vo to Vi is very large, indeed it is equal
to the open loop gain A. For a 741 op-amp powered with VCC= +10V and VEE= -10V,
Vo will saturate (reach the maximum output voltage range) at about ±10 V. With an
A=200,000V/V saturation occurs with an input differential voltage of 10/200,000 = 50µV,
a very small voltage.