Analog and Digital Signals
Analog Electronics
Section 2
Prof. Dr. Murat Akar
D-211
E-mail: askar@eee.metu.edu.tr
Web: www.eee.metu.edu.tr/~askar
Analog Signals are links to the real world
Transreceiver
Bio-eng: Neuronal implants
Linear Amplifiers (1)
Multiply amplitude of a signal by a constant scalar quantity
xo(t) = A xi(t)
Non-scalar or
non-uniform
amplification
is called
distortion
Linear Amplifiers (2)
Symbol for a single-ended
input linear voltage amplifier.
Transfer Characteristics (1)
Plot of amplifier output versus amplifier input
Ideally provides linear
voltage gain regardless of
the amplitude of the input
signal
Real amplifiers have power
supplies that limit the
amplitude of the output
If input is too large, output
clamps
Transfer Characteristics (2)
Real Transfer Characteristics
Each circle represents
a different DC
component for the
input and output
signals called an
operating point
Location of operating
point has an effect on
Gain = Slope
To operate amplifier in its linear region, the input
must be kept small enough
Operating Point (1)
Voltage gain, output DC voltage, allowable input
magnitude range are affected
input signal range
amplifier gain magnitude
amount of distortion
Operating Point (2)
Input and output signal amplitude ranges are
maximized when operating point is near middle of
linear region
Derivative of
transfer
characteristic
gives measure
of amplifier gain
linearity (and
distortion)
Signal Convention (1)
Signal Convention (2)
In general
DC magnitudes in uppercase symbol and
subscript
Example: ID, VD
Ac signal quantities in lowercase symbol &
subscript
Example: id(t), vd(t)
Total DC + ac signal quantities in lowercase
symbol, uppercase subscript
Example: iD(t), vD (t)
vD(t) = VD + vd(t)
iC(t) = IC + ic(t)
Superposition
Amplifier Classification
If the amplifier is linear, superposition can be
applied. Each component can be determined
seperately.
Determine the DC magnitude of the output using
DC model (i.e capacitors are open circuited,
inductors are short circuited)
Example: IO, VO
Determine the ac signal component of the output
using the ac model (i.e., DC sources are killed and
capacitors are short circuited, inductors are open
circuited) as
Example: vo(t) = Av vi(t)
Input
Output
Type
Voltage
Voltage
Voltage
Voltage
Current
Transconductance
Current
Voltage
Transresistance
Current
Current
Current
Ideal Voltage Amplifier
+
+
vi
-
Avi
+
vo
-
Real Voltage Amplifier
+
vi
-
Ri
Ro
Avi
+
vo
-
Loaded Ideal Voltage Amplifier
+
vs
Rs +
vi
-
Avi
+
vo
-
RL
vo
= A
vs
Loaded Voltage Amplifier
+
Rs +
vi
-
vs
Ri
+
vo
-
Ro
Avi
Ideal Current Amplifier
ii
RL
ii
Loaded Ideal Current Amplifier
+
vi
-
ii
Rs
ii
ii
io
Ri
Aii
io
Ro
Loaded Current Amplifier
is
RL
RS
ii
Ri
Aii
io
Ro
RL
io
= A
is
io
Rs
Ro
= A
is
R s +R i R o +R L
To determine Input Resistance Ri
To determine Output Resistance Ro
Ri
+
vo
-
Ro
Avi
Voltage Amplifier
+
vi
-
Aii
io
Real Current Amplifier
vo
Ri
RL
= A
vs
Rs +R i R o +R L
is
Aii
Ri
Aii
Current Amplifier
io
Ro
Apply input voltage vi
(or input current ii)
Determine the input
current ii (or input
voltage vi)
Then
Ri = v i / ii
+
vi
-
ii
Ri
Ro ix
Avi
+
vx
-
Voltage Amplifier
+
vi
-
ii
Ri
Aii
Current Amplifier
ix +
Ro vx
-
Kill the input signal
(set vi or ii to zero)
Apply a test voltage
vx to the output node
Determine the current
ix that the source
delivers to the circuit
Then
Ro = v x / ix
