Introduction to Microelectronics
Chapter 7
F
REQUENCY
A
NALYSIS
FOR
F
IRST
O
RDER
C
IRCUITS
7.1
From Quasistatic to SingleTimeConstant Circuits
Up to now we have only considered the
quasistatic
behavior of the transistor circuit.
That is, the transistors are SO fast that they can reach steady state for the time period of interest
or sampling.
In this chapter, we would like to derive the lower bound in time (or upper bound in
frequency) where this approximation remains valid.
Since the circuit module we have
considered until now is rather small, the time delay is basically caused by the RC (resistor
capacitor) effect, because the inductance or the transmission line effect is negligible in small
circuit modules. Our goal is to match the smallsignal amplifier circuit to a lowpassfilterlike
transfer function where there is only the
single time constant (STC)
(called the
dominant pole
)
that governs the deviation from the quasistatic characteristics.
As shown in Fig. 7.1, although
there are many other useful frequency responses from filter or bandpass circuits, the amplifier
circuits in consideration will only be mapped to the lowpass response in Fig. 7.1(a).
Conventionally, the amplification factor is expressed in unit of dB (decibel):
A
(unitless)
⇒
20
×
log
10
A
(dB)
(7.1)
The use of log is to convert multiplication of cascading amplifiers of
A
1
×
A
2
to log
10
A
1
+
log
10
A
2
, and the number 20 is arbitrarily chosen in the early days to give enough precision by
using integers only.
A few convenient numbers to remember:
A
= 1 = 0dB;
A
=
2
= 3dB;
A
=
2 = 6dB;
A
= 10 = 20dB;
A
= 100 = 40dB;
A
= ½ =

6dB;
A
= 0.1 =

20dB.
Fig. 7.1.
Frequency responses of an amplified (a) lowpass; (b) highpass; (c) bandpass networks.
For the amplified lowpass network in Fig. 7.1(a), we denote the
corner frequency
f
C
(or
Edwin C. Kan
Page
71
3/26/2010
A
(dB)
f
(Hz)
f
C
f
T
(a)
A
(dB)
f
(Hz)
(b)
A
(dB)
f
(Hz)
(c)
A
A
v
in
v
out
v
in
v
out
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Introduction to Microelectronics
called knee frequency) as when
A
decreases 3dB.
For frequency below
f
C
, we can assume that
the circuit has quasistatic behavior, although we need to be a bit more conservative if phase of a
sinusoidal input is considered.
This point will be clear in the next section.
We will first examine the capacitance from the physical aspects of the transistors, and
build these capacitors into the smallsignal transistor models.
We will then obtain the transfer
function of the singlestage amplifiers to estimate their dominant poles and corner frequency.
7.2
Capacitance in MOSFET
The cross section of a pair of adjacent PMOS and NMOS transistors are shown in Fig.
7.2 as an illustration.
Different technologies may have rather different geometry, such as deep
trench isolation trench instead of shallow trench isolation, twinwell instead of nwell, and the
substrate is replaced by silicon on insulator (SOI).
Here, the NMOSFET is sitting on the p
substrate, and PMOSFET is sitting within an n well.
If the psubstrate is kept at GND and nwell
at
V
DD
, then a reverse bias exists to electrically isolate the two transistors.
Notice that this
practice gives no forwardbias junction in CMOS except for the one induced by gate.
This is the end of the preview.
Sign up
to
access the rest of the document.
 Spring '07
 SPENCER
 Microelectronics, Electronics terms, Cutoff frequency, CGD, Edwin C. Kan

Click to edit the document details