Notesale: Turn your study into money

Document Preview

Extracts from the notes are below, to see the PDF you'll receive please use the links above

---

PHYS 331: Junior Physics Laboratory I

Notes on Analog Circuits
Digital circuits deal, in principle, with only two values of voltage, whereas analog circuits
process signals with continuous variation of voltage
...

These notes will provide a very basic introduction to the capabilities of analog circuitry
...

A
...
They, in turn,
depend upon the ability to fabricate semiconducting materials to very precise specifications
...
Descriptions of
other types of transistors and more quantitative treatments can be found in the suggested
readings
...
(Commercially important semiconductors include the elements silicon and
germanium, and compounds gallium arsenide and gallium phosphide
...
Semiconductors are technically useful because the
density of charge carriers, and hence the conductivity, is exquisitely sensitive to part-per-million
levels of impurities, referred to as "dopants"
...
A specimen with predominantly
positive charge carriers is referred to as "p-type", while a specimen with negative carriers is "ntype"
...
The positive carriers are "holes", empty
states in an otherwise filled sea of electrons
...
A
complete explanation can be found in any solid state physics text
...
If wires are attached to the sandwich, as indicated
in Fig
...
The resulting
device is called a "diode"
...
First, there is a threshold (about 0
...
1 Junction diode structure, circuit symbol and I-V characteristic
...
This threshold is the "junction voltage drop" or just "junction drop"
...
Second, there is a small "leakage current" when the diode is "reverse biased" (n
side positive with respect to p side)
...

A more interesting device can be made by joining three layers as shown in Fig
...
(The term "bipolar" refers to the use of both n and p-type
material in the structure
...
Other designs are possible, but will not be discussed here
...
The unexpected fact is that if
the collector is made positive with respect to the emitter, then a current in the base-emitter circuit
can control the current flow across the (reverse biased) collector-base junction
...
This current gain actually represents a
power gain, in the sense that a low-power input signal applied to the base can cause a higherpower signal to appear in the collector circuit
...
2 NPN junction transistor structure and circuit symbol
2

C

B
...
3, which shows the commonemitter configuration of an NPN transistor
...
If Vin
is zero or negative there will be no base current, hence no collector current, and the transistor is
said to be cut off
...
6 V for silicon), base
current will start to flow, the collector current will increase according to Eq
...
For sufficiently large IB, V CE reaches a minimum (0
...
2 V for silicon) and I C is
limited chiefly by the load resistor R2
...

The ability to switch between two well defined states is ideal for implementing digital logic
...
Suppose
we define logic 0 as a zero-volt signal and logic 1 as VCC, a positive voltage
...
3, when V in = 0 the transistor is cut off and Vout = V CC
...
Vout is then nearly zero
(actually VCE at saturation)
...

A NOR circuit can be constructed using two transistors in common emitter
configurations, as shown in Fig
...
A logic high applied to either input (or both) turns on Q1 or
Q2, pulling the output low, which is the required function
...

The TTL circuits used for the digital exercises also employ transistors as switches,
although the circuit configuration is somewhat different to facilitate manufacture
...


V CC
R

2

IC
V out

V in

R1
IB

V CE
V BE

IE = IB + IC

Fig
...
4 Two-transistor NOR gate and conversion to OR
...
Single-stage amplifiers
The common emitter configuration can be modified to produce an output signal that is
linearly proportional to the input, a function known as amplification
...
The signal
current is then superimposed on the constant bias current
...
Figure 5 presents the same argument graphically, and Fig
...
5 Plot of collector current vs base current showing effect of bias and signal inputs
...
Addition of a varying
component causes the collector current to follow within the limits shown
...
6
...
A capacitor is used to couple in the AC signal so
that the signal source cannot affect the bias current
...

implementation
...

The output voltage of the common emitter amplifier can be substantially larger than the
input voltage
...

A small positive signal input will cause additional base current to flow, which causes a much
larger increase in the collector current, increasing the voltage drop across the collector resistor
and lowering the output voltage
...
The output voltage is therefore an inverted and amplified
replica of the input, offset by a DC component due to the bias current
...
A detailed analysis shows that the
gain is determined by hFE and by the effective resistances at input and output
...
6 is not actually essential for circuit function, but it
does serve a very useful purpose
...
The current gain hFE increases at higher temperatures, resulting in still more
collector current for the same bias current, further increasing the temperature
...
At best, it will shift the operating point toward saturation and may make the
circuit inoperative
...
7 The emitter-follower circuit
...
The decrease in VBE decreases the
base current, partially compensating for the increased hFE and thereby stabilizing the circuit
...
Practically, an RE much
smaller than RC is usually sufficient for stability
...
If the signal
source cannot supply the power, the emitter follower circuit in Fig
...
A small current
from the signal source, applied to the base, can cause a large amount of current to flow through
the emitter resistor or a load connected in parallel with it
...
It can be shown that the output voltage is only equal to the input voltage, minus the drop
in the base-emitter diode, so there is no voltage gain
...

As drawn, the emitter follower can connect the load to the positive supply, but it cannot
produce negative output voltages
...
If the circuit
is intended for high power this implies large dissipation in the emitter resistor even in the
absence of a signal
...
8
...
With no input there is no collector current
and hence no dissipation at all in the absence of a signal
...
This circuit is
called a push-pull emitter follower, or a complementary pair, and is widely used as the output
stage of relatively high power amplifiers
...
8 A simple push-pull circuit, without bias
...
As
in the common emitter amplifier, thermal runaway can be avoided by a small emitter resistor,
typically an ohm or two, in each emitter lead
...

The circuit does not, therefore, produce an output until the input is bigger than about 0
...
One cure is to bias the transistors so that they are on the verge

+V CC
R
Q1
RE
Vin
R
Q

E

R load

2

R
-V EE
Fig
...

7

of conduction without a signal
...
9, where diodes are used to set the base
voltage exactly one diode drop above or below zero
...

The magnitude of voltage or power gain available from a single stage of amplification is
obviously limited, so most practical amplifiers consist of several coupled stages
...
Such complex devices are usually purchased, rather than being
designed by an experimentalist, so they will not be considered here
...
Oscillators
An oscillator circuit converts DC electrical energy into a periodic signal
...
If, for some
frequency, the feedback is in phase at the input, and if the power gain around the loop is greater
than one, the output will be a self-sustaining oscillation at the favored frequency
...

Fig
...
The Colpitts circuit is based on a biased emitter follower stage
...
Coupling capacitor CC is included to block the DC path through the feedback circuit,
thereby maintaining the desired bias level
...
Single-transistor oscillator circuits: (a) Colpitts, (b) Hartley
8

amplifier, with an LC circuit replacing the collector resistor and with a transformer-coupled
output
...
By coupling some of the output into the emitter circuit,
CF causes the base-emitter voltage to vary slightly, modulating the base current and sustaining
the oscillation at the LC resonant frequency
...

Any amplifier circuit may become an oscillator if stray inductance or capacitance,
perhaps within the transistor structure, in a breadboard or in a power supply, provides positive
feedback at any frequency for which the gain is sufficiently large
...
At high frequencies it may be necessary to
divide the necessary gain across several stages, each of which is carefully isolated from adjacent
stages
...
Operational Amplifiers
Operational amplifiers are multi-stage differential amplifiers characterized by high gain,
high input impedance and wide bandwidth
...
Op-amps are
often used as building blocks to create functions needed by specific experiments in much the
same way that packaged gate circuits are used to synthesize digital logic
...

General purpose op-amps have two inputs, labeled + and -, and a single output
...
Because of the high gain, a very small
difference in voltage at the input terminals will drive the amplifier to full output
...
The effect of
an ideal amplifier on the feedback circuit can be understood by applying two rules: (1) The
output changes in such a was as to make the voltage difference between the inputs zero; (2) The
inputs draw no current
...
11(a) provides a simple example for analysis
...
Using Ohm's law to get the individual currents then gives the relation

9

Rf

Vi

Ri
Ii

V i1

If
+

V i2

Vo

V i3
(a)

R i1
R i2
R i3

Rf
+

Vo

(b)

Fig
...


Ii =

Vi V V Vo
=
= If
Ri
Rf

(2)

The first rule requires V- = 0, so this simplifies to

Vo =

Rf
Ri

Vi

(3)

which tells us that the gain of the circuit is determined by the resistances and not by the
amplifier, whose gain may vary from unit to unit
...

The same analysis applied to the circuit of Fig
...
The advantage of this circuit over a passive resistive
combiner is that there is no interaction among the input signals
...

It is also possible to construct a non-inverting circuit, as shown in Fig
...
The voltage
at the inverting terminal is determined by the R1, R2 voltage divider
V =

R2
V
R1 + R2 o

(5)

Rule 2 requires that the amplifier adjust Vo until V- = Vi, so

10

Vi

+
-

R2

+
-

Vi

Vo

Vo

R1
(a)

(b)

Fig 12 (a) A non-inverting amplifier or follower with gain
...

Vo = 1 +

R1
V
R2 i

(6)

Again, the voltage gain is determined by a resistance ratio, but there is no inversion
...
Alternatively, if we let R1
become very small and R2 become very large, we arrive at the circuit of Fig
...
This is called
a follower, because the output voltage 'follows' the input voltage
...

A combination adder/subtractor, usually called a differential voltage amplifier, is shown
in Fig
...
Applying the rules, one can show that the output is proportional to the difference
between the voltages at the inputs:
Vo =

R2
(Vi2
R1

Vi1 )

(7)

This is useful in situations where the signal source is 'floating', that is when both terminals are at
some potential above ground and the desired signal is their voltage difference
...
13 One implementation of a differential amplifier
...
14 (a) A pure integrator or low-pass filter
...

this particular circuit is that it becomes inaccurate if the resistors are not exactly equal as
assumed
...

There are even more interesting possibilities if we allow frequency-dependent feedback
...
14(a)
...
(3) is applicable, provided we
substitute the complex impedance of the feedback capacitor for the simple resistance term
...
(This usage is conventional in electrical engineering, to avoid
confusion with currents
...
The circuit is therefore a filter that passes low frequencies and attenuates
high frequencies
...
Start with
the fundamental equations for a capacitor

CV = Q

I=

dQ
dV
=C
dt
dt

(9)

and then invoke the second rule to equate the input current to the feedback current
Vi
dV
= Cf o
Ri
dt

(10)

This equation can be integrated to yield
12

1
Ri C f

t
0

Vi dt = Vo

(11)

which tells us that we have built an integrator
...

Although the integrator is a low-pass filter, the infinite gain at DC means that any small
offset will accumulate until the amplifier saturates
...
14(b)
...
Many other filter
circuits with advantageous characteristics for particular applications are possible, but we will not
consider them here
...
15(a) is useful with transducers that produce a current, rather than a
voltage output
...
Following the rules, the
amplifier adjusts Vo so that all the current flows through Rf ,V- = 0, and the output voltage is

Vo = R f Ii

(13)

Logically the 'gain' of this current to voltage converter would be expressed in ohms, but it is
more common and convenient to use volts/amp
...
15(b) is also a
current-voltage converter, but here the voltage drop across the transducer decreases as the current

+V CC

+V CC

Rf
Ii

+

Vo
(a)

Vo
R
(b)

Fig
...

13

increases
...

A typical integrated-circuit op-amp can produce output currents up to a few milliamps
and output voltages to nearly the supply voltages
...
The push-pull booster shown in Fig
...
Note
that the feedback for the inverter is taken around the booster, not just the op-amp
...

Rf

Vi

Ri

+V CC

+

Vo

-V EE

Fig
...


14



---