UNIVERSITY OF CALIFORNIA, SAN DIEGO
Department of Electrical and Computer Engineering
Bang-Sup Song
1
ECE163
Lecture #1: Feedback Amplifier Stability
v
i
i
i
Network
v
i
i
i
Network
v
o
i
o
One-port network
Two-port network
Fig. 1.1: Driving-point and transfer concepts.
Driving-Point and Transfer Functions
Consider any networks with one port or two ports as shown in Fig. 1.1.
On each port,
we can define its terminal voltage and the current flowing into the terminal.
In the one-
port case shown on the left side, the ratio of the terminal voltage to the current can be
defined.
R s
( )
=
v
i
s
( )
i
i
s
( )
,
and
G s
( )
=
i
i
s
( )
v
i
s
( )
.
(1.1)
The former is driving-point resistance, and the latter one is driving-point conductance.
Their units are
±
and 1/
±
, respectively.
That is, if the input and output are referred to the
same port, the term “driving-point” is used.
On the other hand, in the two-port case
shown on the right side, the following four ratios can be defined.
A
v
s
( )
=
v
o
s
( )
v
i
s
( )
,
A
i
s
( )
=
i
o
s
( )
i
i
s
( )
,
R s
( )
=
v
o
s
( )
i
i
s
( )
,
and
G s
( )
=
i
o
s
( )
v
i
s
( )
,
(1.2)
where A
v
(s) and A
i
(s) are unit-less transfer functions defined as voltage and current
gains, respectively.
The latter two definitions are the same as in (1.1) for the one-port
network, but they are called as trans-resistance and trans-conductance, respectively.
The
term “trans” is now used since the input and output ports are different.
In steady-state small-signal analysis, impedances of reactive components such as
inductor and capacitor are frequency-dependent as sL and 1/sC, where s is the complex
frequency of j
²
.
The unit of
²
is rad/sec.
Note that the angular frequency
²
is defined
as the amount of angle rotation per second, while the ordinary frequency unit in Hertz
(Hz) is defined as the number of rotations per second.
Since one rotation of a vector
covers an angle of 2
³
radian, there is a 2
³
difference between
²
and f like
²
= 2
³
f.
In
general, all these transfer functions can be represented as a ratio of two polynomial
functions N(s) and D(s) in steady state.
Let’s consider a general transfer function H(s) as
follows.

This
** preview**
has intentionally

**sections.**

*blurred***to view the full version.**

*Sign up*