1. Analog electronics - syllabus
2. Introduction
Part I of this syllabus deals with the basic electronic devices, and fundamental
circuit configuration and characteristics. Second part deals with more complex
analog circuits, of witch amplifiers are a very significant category.
Introduction chapter cover the general feedback theory concept, witch is used
extensively in analog circuits to set or control gain values more precisely, and to
alter, in favorable way, input and output impedance.
First chapter introduces the ideal op-amp concept and related circuits (op-amp
applications). The op-amp is the most common analog integrated circuits.
Second chapter presents IC biasing technique, advance concepts witch primarily
uses constant-current sources and differential and multistage amplifiers.
Chapter 3 present’s ac and dc effects in analog integrated circuits for non-ideal
op-amp and the impact of such effects on op-amp applications.
Applications and design of integrated circuits are presented in chapter 4. Such
applications are Schmitt trigger circuits, rectifier circuits, voltage regulators, and
active filters.
1. Ideal op-amp model
Definition:
An operational amplifier (op-amp) is an integrated circuit that amplifies the
difference between two input voltages and produces a single output.
From signal point of view, the op-amp has two input terminals and one output
terminal, as shown in the small-signal circuit symbol shown in figure 1(a).
The op-amp also requires dc power, as do all transistor circuits, so that the
transistors are biased in the active region. Also, most op-amps are biased with
both a positive and negative voltage supplies, as indicated in figure 1(b).
V+
1
3
2
+
+
V-
Figure 1. (a) Small-signal circuit symbol of op-amp (b) op-amp with
positive and negative supply voltage
Terminal (1) is called inverting input terminal designed by the “-“ notation, and
the terminal (2) is the noninverting input terminal designed with “+” notation.
Terminal (3) represents the output terminal.
2. Ideal parameters:
The ideal op-amp senses the difference between two input signals and amplifiers
this difference to produce an output signal. The terminal voltage is the voltage at
a terminal measured with respect to ground. The ideal op-amp equivalent circuit
is show in figure 2 (a).
Ideally, the input impedance is infinite, witch means that the input current is zero.
The output terminal acts as the output of an ideal voltage source, meaning that
the small signal output impedance is zero.
The parameter Aod show in the equivalent circuit is the differential gain of the
op-amp.
Vo
~ 1-2 V
+
V
V1
Slope = Aod
Vo
(V2-V1)
Aod(V2-V1)
+
V2
V~ 1-2 V
Figure 2. (a) Ideal op-amp equivalent circuit and (b) op-amp transfer
characteristic
Since the ideal op-amp responds only to the difference between the two input
signals V1 and V2, the ideal op-amp maintains a zero output signal for V1 = V2.
When V1=V2 ≠ 0 there is what is called a common-mode input signal. For the
ideal op-amp, the common-mode output signal is zero. This characteristic is
referred to as common-mode rejection.
Because the device is biased with both positive and negative power supplies,
most op-amps are directed-coupled devices (no capacitors are used on the input)
then the input voltage (V1 or V2) can be dc voltage, witch will produce and de
output voltage Vo.
Since op-amp is composed of transistors biased in the normal active region by
the dc-input voltage V+ and V-, the output voltage is limited. When the output
voltage approaches V+, it will be saturate, or be limited to a value nearly equal to
V+. Similar is happened with V-.
The output saturation voltage vary from op-amp to another, but in general the
output voltage is limited to V-+∆V < Vo < V+ -∆V where ∆V is generally between 1
and 2 V.
Review:
Ideal op-amp characteristics are:
•
infinite input impedance – which means that the input current through
the input terminals is zero
•
zero output impedance – witch means that the output voltage through
a load impedance is the same as without load impedance
•
differential gain (conversely name as open loop gain) is considered
infinite – witch means that the output voltage have a linear
dependence related with the input differential voltage. Also the
differential input voltage can be considered practically zero in case
when op-amp works linear.
3. Inverting amplifier
One of the most widely used op-amp circuits is the inverting amplifier. The
closed loop configuration is showed in figure 3 with op-amp equivalent circuit.
The closed-loop gain or simply the voltage gain is defined as:
i2
R2
i1
Vi
R1
Vo
Figure 3. Inverting amplifier
As we said if open-loop gain Aod is very large, then the two inputs V1 and V2
must be nearly equal. Since V2 is at ground potential, voltage V1 must also be
approximately zero volts. We can introduce the virtual ground concept – there is
not a physical connection to the ground, only the node potential has the ground
potential (or better said > the potential is essentially zero, but it dose not provide
a current path to the ground).
We can write then:
V1
Vi
=
R1
R1
Since the current into the op-amp is assumed zero, current i1 must flow trough
resistor R 2 to the output terminal, which means i1=i2
i1 = Vi -
The output voltage is given by:
Vo = Vi – i2R2 = 0 -
V1
R1
R2
therefore the closed-loop gain is:
R2
R1
We observe that the closed-loop gain is a function of the ratio of two circuit
resistance, it is not a function of the transistor parameter within the op-amp
circuit.
Av = -
The minus sign implies a phase reversal. If the input voltage V1 is positive then
the output voltage Vo must be negative or below to zero. Also note that if the
output terminal is a open-circuited, current i2 must flow back into the op-amp.
However, since output terminal impedance for the ideal case is zero, the output
voltage is not function of this current that flow back into the op-amp and is not
dependent of the load.
We can also write the input impedance seen by the voltage source V1.
Because of virtual ground we have:
Vi
iI =
R1
So the input impedance is defined as:
Vi
Ri =
= R1
ii
This shows that the input impedance seen by the source is a function of
R1 only, and is a result of the virtual ground concept.
3. Amplifier with a T-network
Assume that an inverting amplifier is to be designed having a closed-loop voltage
gain Av=-100 and an input resistance of Ri=R1=50 KΩ. The feedback resistance
must have then 5 MΩ. This value is too large for most practical circuits.
Consider then a new op-amp circuit shown in figure 4 with a T-network in the
feedback loop. The analysis of the circuit is similar to that of the inverting
amplifier circuit.
At the input we have:
Vi
i1 = i2
R1
We can also write that
R2
R1
If we sum the currents at the node Vx , we have
Vx=0-i2R2= - Vi
i2+i4=i3
which can be written
-
Vx
R2
-
Vx
R4
Vx-Vo
R3
=
or
Vx (
1
R2
+
1
R4
1
R3
+
Vo
R3
)=
Substituting the expression of Vx in equation 2, we obtain
R2
1
1
1
Vo
+
+
)
(
)
-Vx ( R
=
R2
R4
R3
R3
1
Then the closed-loop voltage gain will be
Av =
Vo
Vi
=-
R2
R1
(
1
R3
R4
+
+
R3
R2
)
The advantage of T-network is the fact that all resistance used is into a
reasonable value domain.
i2
i3
R2
R3
i2
i1
R4
0
Vi
R1
Vi = 0
0
Figure 4. Inverting op-amp with T-network
Vo
4. Noninverting Amplifier
In our previous discussions, the feedback element was connected between the
output and the inverting input terminal. However, a signal can be applied to
noninverting input terminal while still maintaining negative feedback.
Basic noninverting amplifier is shown in figure 5. The input voltage Vi is applied
directly to the noninverting terminal, while one side of resistor R1 is connected to
the ground and to the inverting op-amp terminal.
i2
R2
i1
Vo
R1
Vi
Figure 5. Noninverting op-amp circuit
A similar principle as virtual ground concept can be applied also here, between
the two op-amp inputs. Now the difference is the fact that the noninverting
terminal has a potential different the zero actually is V1. Also we can remember
for an ideal op-amp, V1=V2, which creates a virtual short circuit between the
input terminal. Yet, in the equivalent ideal op-amp circuit presented in Figure 1, a
short circuit obviously does not exist between the input terminals. Instead, the
two inputs appear to be virtually shorted together, since there is no current path
between them.
The analysis of noninverting amplifier is essentially the same as for inverting
amplifier. We assume that no current enters into the input terminals. We can
write then:
i1= -
V1
R1
=-
Vi
R1
Current i2 is given by:
V1 -Vo
V-V
i2= =- I o
R2
R2
But in the same time i1=i2 then:
VI
VI - Vo
=
R1
R2
Solving the equation for the closed-loop voltage, we find:
R2
Av= 1 +
R1
From this equation, we see that the output is in phase with the input, as
expected. Also note that the gain is always greater the unity.
The input signal VI is connected directly to the noninverting terminal
therefore, since the input current is essentially zero, the input impedance seen by
the voltage source is very large, ideally infinite.
5. Voltage Follower
An interesting property of the noninverting amplifier occur when R2=0. The
closed-loop voltage gain then becomes
Av= 1
Since the output follows the input, this op-amp circuit is called a voltage
follower. The closed-loop voltage gain is independent of resistor R2 (except
when R1=0), so we can set R1=∝ to create an open circuit (figure 6). It this
configuration useful?
Vo
Vi
Figure 6. Voltage follower
Other terms for voltage follower are impedance transformer or buffer. The
input impedance is essentially infinite and the output is essentially zeroed. If, for
example, the output impedance of a signal source is large, a voltage follower
inserted between source and load will prevent the loading effects, that is, it will
act as a buffer between the source and the load.
Consider the case of a voltage source with a100KΩ output impedance driving a
1KΩ load impedance, as shown in figure 6. This situation may occur if the source
is a transducer. The ratio output voltage to input voltage is:
Vo
RL
1
=
=
= 0.01
Vi
RL+RS
1+100
The equation indicates that, for this case, there is a severe loading effect, or
attenuation, in the signal voltage.
Using a voltage follower circuit between source and the load (since Vo=Vi) the
loading effect is eliminated.
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Analog electronics - syllabus.................................................................................................................................1
Introduction ..............................................................................................................................................................1
Ideal op-amp model.................................................................................................................................................2
Ideal parameters:......................................................................................................................................................2
Inverting amplifier...................................................................................................................................................4
Amplifier with a T-network...................................................................................................................................5
Noninverting Amplifier ..........................................................................................................................................7
Voltage Follower.....................................................................................................................................................8