Neamen D. Microelectronics: Circuit Analysis and Design

Подождите немного. Документ загружается.

1098 Part 2 Analog Electronics

Consider the oscillator in Figure 15.35. Design the circuit to oscillate at

= 1 kHz

Solution: Using Equation (15.88), we can write

2.2 f

2.2(10

)

= 4.55 ×10

−4

= 0.1 μF

, then

= 4.55 k

Trade-offs: Using standard-valued elements with values of

= 0.082 μF

and

= 5.6k

produces an oscillation frequency of 990 Hz, within 1% of the speci-

ﬁed value. If element tolerance values are taken into account, a potentiometer may

have to be used to produce the 1000 Hz oscillation frequency.

Comment: A larger frequency of oscillation can easily be obtained by using a

smaller capacitor value.

EXERCISE PROBLEM

*Ex 15.8: For the Schmitt trigger oscillator in Figure 15.35, the saturation out-

put voltages are

+10

V and

−5V

= R

= 20 k

= 50 k

, and

0.01 μF

. Determine the frequency of oscillation and the duty cycle. Sketch

and

versus time over two periods of the oscillation. (Ans.

f = 866 Hz

,duty

cycle

= 39.7%

)

Monostable Multivibrator

A monostable multivibrator has one stable state, in which it can remain indeﬁnitely

if not disturbed. However, a trigger pulse can force the circuit into a quasi-stable state

for a deﬁnite time, producing an output pulse with a particular height and width. The

circuit then returns to its stable state until another trigger pulse is applied. The mono-

stable multivibrator is also called a one-shot.

A monostable multivibrator is created by modifying the Schmitt trigger oscilla-

tor as shown in Figure 15.37. A clamping diode

is connected in parallel with

In the stable state, the output is high and voltage

is held low by the conducting

diode

15.4.2

–

Figure 15.37 Schmitt trigger monostable multivibrator

nea80644_ch15_1061-1140.qxd 07/12/2009 3:58 Page 1098 pinnacle MHDQ-New:MHDQ134:MHDQ134-15:

Chapter 15 Applications and Design of Integrated Circuits 1099

The trigger circuit is composed of the capacitor

, resistor

, and diode

and is connected to the noninverting terminal of the comparator. The value of

chosen to be much larger than

, so that voltage

is determined primarily by a

voltage divider of

and

. We then have

∼



+ R



≡ β V

(15.89)

where

is the sum of the forward and breakdown voltages of

and

,or

= (V

γ 1

+ V

)

. This voltage is the positive saturated output voltage.

The circuit is triggered by a negative-going step voltage applied to capacitor

This action forward-biases diode

and pulls the voltage

below

. Since the

comparator then sees a larger voltage at the inverting terminal, the output switches to

its low state of

=−V

=−(V

γ 2

+ V

)

Voltage

then becomes

∼

−



+ R



≡−βV

(15.90)

causing

to become reverse biased, thus isolating the oscillator circuit from the

input triggering network. The negative-step change in

causes voltage

to de-

crease exponentially with a time constant of

= R

toward a ﬁnal value of

−V

. Diode

is reverse biased during this time. When

drops just below the

value of

given by Equation (15.90), the output switches back to its positive satu-

rated value of

. The capacitor voltage

then starts to increase exponentially

toward a ﬁnal value of

. When

reaches

, diode

again becomes forward

biased,

is clamped at

, and the output remains in its high state.

The waveforms of

and

versus time are shown in Figure 15.38. After the

output has switched back to its high state, the capacitor voltage

must return to its

quiescent value of

= V

. This implies that there is a recovery time of



− T )

during which the circuit should not be retriggered.

For

t > 0

, voltage

can be written in the same general form as Equation (15.82),

as follows:

=−V

+(V

−(−V

))e

−t/τ

(15.91)

0 T ′

Toward

–V

Toward

–V

(a)

(b) (c)

Figure 15.38 Schmitt trigger monostable multivibrator voltages versus time (a) input trigger

pulse, (b) capacitor voltage, and (c) output pulse

nea80644_ch15_1061-1140.qxd 07/12/2009 3:58 Page 1099 pinnacle MHDQ-New:MHDQ134:MHDQ134-15:

1100 Part 2 Analog Electronics

where

= R

. At

t = T

=−βV

and the output switches high. The pulse

width is then

T = τ



1 + (V

)

(1 − β)



(15.92)

If we assume

 V

and if we let

= R

such that

β = 1/2

, then the pulse

width is

T = 0.69τ

. We can show that for

 V

and

β = 1/2

, the recovery time



− T ) = 0.4τ

. There are alternative circuits with shorter recovery times, but

we will not consider them here.

DESIGN EXAMPLE 15.9

Objective: Design a monostable multivibrator to produce a given pulse width.

Speciﬁcations: The circuit with the conﬁguration shown in Figure 15.37 is to be de-

signed to produce an output pulse that is

1 μs

wide. Assume parameters of

=10 V

= 0.7V

and

= R

= 20 k

Choices: Assume an ideal comparator is available. Use standard-valued element val-

ues in the ﬁnal design.

Solution: Since

 V

and

= R

, then from Equation (15.92), we have

T = 0.69τ

= R

0.69

= 1.45 μs

= 10 k

, then

= 145 pF

Trade-offs: Using standard-valued elements of

= 10 k

and

= 150 pF

pro-

duces a pulse width of

1.035 μs

. Element tolerances must also be taken into account

in the ﬁnal design.

Comment: In actual monostable multivibrator ICs,

and

are external elements

to allow for variable times.

EXERCISE PROBLEM

*Ex 15.9: For the monostable circuit shown in Figure 15.37, the parameters are:

= 12 V

= 0.7V

= 0.1 μF

= 10 k

, and

= 90 k

. (a) Find

the value of

that will result in a 50

s output pulse. (b) Using the results of part

(a), ﬁnd the recovery time. (Ans. (a)

= 3.09 k

(b) 47.9

The 555 Circuit

The 555 monolithic integrated circuit timer was ﬁrst introduced by Signetics

Corporation in 1972 in bipolar technology. It quickly became an industry standard

for timing and oscillation functions. Many manufacturers produce a version of a

555 IC, some in CMOS technology. The 555 is a general-purpose IC that can be used

15.4.3

nea80644_ch15_1061-1140.qxd 07/12/2009 3:58 Page 1100 pinnacle MHDQ-New:MHDQ134:MHDQ134-15:

Chapter 15 Applications and Design of Integrated Circuits 1101

The RS ﬂip-ﬂop is a digital circuit that will be considered in detail in a later

chapter. Here, we will describe only the basic digital function of the ﬂip-ﬂop, so that

the operation of the 555 timer can be explained. When the input

is high and input

is low, output

is high. The complementary state occurs when

is low and

high, producing a low

output. If both

and

are low, then output

remains in

its previous state.

Comparator 1 is called the threshold comparator, which compares its input

with an internal voltage reference set at

(

by the voltage divider

, and

When the input level exceeds this reference level, the threshold comparator output

goes high, producing a high output at ﬂip-ﬂop terminal

. This turns the discharge

transistor on and an external timing capacitor (not shown in this ﬁgure) starts to

discharge.

Flip-flop

(8)

(4)

(3)

(6)

(5)

(2)

(1)

GND

(7)

5 kΩ

100 Ω

Discharge

transistor

Comparator 2

Comparator 1

5 kΩ

Threshold

Reset

Control

voltage

Trigger

Discharge

Buffer

Output

(a)

–

Figure 15.39 (a) Basic block diagram, 555 IC timer circuit and (b) circuit diagram, LM555

timer circuit

for precision timing, pulse generation, sequential timing, time delay generation,

pulse width modulation, pulse position modulation, and linear ramp generation. The

555 can operate in both astable and monostable modes, with timing pulses ranging

from microseconds to hours. It also has an adjustable duty cycle and can generally

source or sink output currents up to 200 mA.

Basic Operation

The basic block diagram of the 555 IC is shown in Figure 15.39(a). The circuit con-

sists of two comparators, which drive an RS ﬂip-ﬂop, an output buffer, and a transis-

tor that discharges an external timing capacitor. The actual circuit of an LM555 timer

is shown in Figure 15.39(b).

nea80644_ch15_1061-1140.qxd 07/12/2009 3:58 Page 1101 pinnacle MHDQ-New:MHDQ134:MHDQ134-15:

1102 Part 2 Analog Electronics

Threshold

Control

voltage

GND

Trigger

Reset

Discharge

5 kΩ

4.7 kΩ

7.5 kΩ

6.2 kΩ

3.9 kΩ

120 Ω

3.3 kΩ

100 kΩ

5 kΩ

Outpu

5 kΩ

1 kΩ

10 kΩ

(b)

Figure 15.39 (continued)

nea80644_ch15_1061-1140.qxd 07/12/2009 3:58 Page 1102 pinnacle MHDQ-New:MHDQ134:MHDQ134-15:

Chapter 15 Applications and Design of Integrated Circuits 1103

The internal control voltage node is connected to an external terminal. This pro-

vides external control of the reference level, should the timing period need to be

modiﬁed. When not in active use, this terminal should be bypassed to ground with a

0.01

F capacitor, to improve the circuit’s noise immunity.

Comparator 2, called the trigger comparator, compares its input trigger voltage

to an internal voltage reference set to

(

by the same voltage divider as before.

When the output trigger level is reduced below this reference level, the trigger com-

parator output goes high, causing the RS ﬂip-ﬂop to reset. Output

goes low and the

discharge transistor turns off. This comparator triggers on the leading edge of a negative-

going input pulse.

The output stage of the 555 IC is driven by output

of the RS ﬂip-ﬂop. This

output is usually a totem-pole push–pull circuit, or a simple buffer, and is generally

capable of sourcing or sinking 200 mA.

An external reset input to the RS ﬂip-ﬂop overrides all other inputs and is used

to initiate a new timing cycle by turning the discharge transistor on. The reset input

must be less than 0.4 V to initiate a reset. When not actively in use, the reset terminal

should be connected to

to prevent a false reset.

Monostable Multivibrator

A monostable multivibrator, also called a one-shot, operates by charging a timing

capacitor with a current set by an external resistance. When the one-shot is triggered,

the charging network cycles only once during the timing interval. The total timing

interval includes the recovery time needed for the capacitor to charge up to the

threshold level.

The external circuitry and connections for the 555 to be used as a one-shot mul-

tivibrator are shown in Figure 15.40. With a high voltage

applied to the trigger

input, the trigger comparator output is low, the ﬂip-ﬂop output

is high, the dis-

charge transistor is turned on, and the timing capacitor

is discharged to nearly

ground potential. The output of the 555 circuit is then low, which is the quiescent

state of the one-shot.

Reset

Ground

Discharge

Threshold

Trigger

555 Output

–

(t)

–

Figure 15.40 The 555 circuit connected as a monostable multivibrator

When a negative-going pulse is applied to the trigger input, the output of the

trigger comparator goes high when the trigger pulse drops below

(

. Output

goes low, which means that the output of the 555 goes high, and the discharge tran-

sistor turns off. The output of the 555 remains high even if the trigger pulse returns

to its initial high value, because the reset input to the ﬂip-ﬂop is still low. The timing

nea80644_ch15_1061-1140.qxd 07/12/2009 3:58 Page 1103 pinnacle MHDQ-New:MHDQ134:MHDQ134-15:

1104 Part 2 Analog Electronics

capacitor charges up exponentially toward a ﬁnal value of

through resistor

The capacitor voltage is given by

v(t) = V

(1 − e

−t/RC

)

(15.93)

When

v(t) = (

, the threshold comparator output goes high, resetting the ﬂip-

ﬂop. Output

then goes high and the output of the 555 goes low. The high output at

also turns on the discharge transistor, allowing the timing capacitor to discharge to

near zero volts. The circuit thus returns to its quiescent state.

The width of the output pulse is determined from Equation (15.93). If we set

v(t) = (

and

t = T

, then





= V

(1 − e

−T/RC

)

(15.94)

Solving for

, we have

T = RC ln(3) = 1.1 RC

(15.95)

The width of the output pulse is a function of only the external time constant

; it is independent of the supply voltage

and any internal circuit parameters.

The triggering input pulse must be of a shorter duration than

. The output pulse

height is a function of

as well as of the internal circuitry. For a bipolar 555, the

output pulse amplitude is approximately 1.7 V below supply voltage

When the output is high and the timing capacitor is charging, another trigger

input pulse will have no effect on the circuit. If desired, the circuit can be reset

during this period by applying a low input to the reset terminal. The output will

return to zero and will remain in this quiescent state until another trigger pulse is

applied.

DESIGN EXAMPLE 15.10

Objective: Design a 555 IC as a monostable multivibrator to produce a speciﬁed

output pulse width.

Speciﬁcations: The circuit with the conﬁguration shown in Figure 15.40 is to be

designed to produce an output pulse width of 100

Choices: A 555 circuit is available. The ﬁnal design is to use standard-valued

elements.

Consider the circuit in Figure 15.40. Let

C = 15 nF

Solution: Using Equation (15.95), we ﬁnd that

R =

1.1C

100 × 10

−6

(1.1)(15 × 10

−9

)

⇒ 6.06 k

Trade-offs: Using standard-valued element values of

C = 12 nF

and

R = 7.5k

will produce an output pulse with a width of 99

s. Element tolerances also need to

be taken into account.

Comment: To a very good approximation, the pulse width is a function of only the

external resistor and capacitance values. A wide range of pulse widths can be ob-

tained by changing these component values.

nea80644_ch15_1061-1140.qxd 07/12/2009 3:58 Page 1104 pinnacle MHDQ-New:MHDQ134:MHDQ134-15:

Chapter 15 Applications and Design of Integrated Circuits 1105

EXERCISE PROBLEM

Ex 15.10: Consider the 555 IC monostable multivibrator. (a) If

R = 20



and

C = 0.012 μ

F, what is the resulting output pulse width? (b) Design the circuit to

produce an output signal with a pulse width of

120 μ

s. (Ans. (a)

T = 0.264

ms;

(b) For example, set

C = 0.01 μ

F, then

R = 10.9

)

Astable Multivibrator

Figure 15.41 shows a typical external circuit connection for the 555 operating as an

astable multivibrator, also called a timer circuit or clock. The threshold input and

trigger input terminals are connected together. In the astable mode, the timing capac-

itor

charges through

= R

until

v(t)

reaches

(

. The threshold compara-

tor output then goes high, forcing the ﬂip-ﬂop output

to go high. The discharge

transistor turns on, and the timing capacitor

discharges through

and the dis-

charge transistor. The capacitor voltage decreases until it reaches

(

, at which

point the trigger comparator switches states and sends

low. The discharge transis-

tor turns off, and the timing capacitor begins to recharge. When

v(t)

reaches the

threshold level of

(

, the cycle repeats itself.

Reset

Ground

Discharge

Threshold

Trigger

555 Output

–

Figure 15.41 Astable multivibrator 555 circuit

When the timing capacitor is charging, during the time

0 < t < T

, the capaci-

tor voltage is

v(t) =

(1 − e

−t/τ

)

(15.96)

where

= (R

+ R

. At time

t = T

, the capacitor voltage reaches the thresh-

old level, or

v(T

) =

(1 − e

−T

/τ

)

(15.97)

Solving Equation (15.97) for the timing capacitor charging time

yields

= τ

ln(2) = 0.693(R

+ R

(15.98)

When the timing capacitor is discharging, during the time

0 < t



< T

,the

capacitor voltage is

v(t



) =

−t



/τ

(15.99)

nea80644_ch15_1061-1140.qxd 07/12/2009 3:58 Page 1105 pinnacle MHDQ-New:MHDQ134:MHDQ134-15:

1106 Part 2 Analog Electronics

where

= R

. At time



= T

, the capacitor voltage reaches the trigger level and

v(T

) =

−T

/τ

(15.100)

Solving Equation (15.100) for the timing capacitor discharge time

yields

= τ

ln(2) = 0.693R

(15.101)

The period

of the astable multivibrator cycle is the sum of the charging period

and the discharging period

. The frequency of oscillation is therefore

f =

+ T

0.693(R

+2R

(15.102)

The duty cycle is deﬁned as the percentage of time the output is high during one

period of oscillation. During the charging time

, the output is high; during the dis-

charging time, the output is low. The duty cycle is therefore

Duty cycle =

×100% =

+ R

+2R

×100%

(15.103)

Equation (15.103) shows that the duty cycle for this circuit is always greater than

50 percent. The duty cycle approaches 50 percent for

 R

and 100 percent for

 R

. Alternative circuits can provide duty cycles of less than 50 percent.

DESIGN EXAMPLE 15.11

Objective: Design the 555 IC as an astable multivibrator for a speciﬁed frequency

and duty cycle.

Speciﬁcations: The circuit with the conﬁguration in Figure 15.41 is to be designed

such that the frequency is 50 kHz and the duty cycle is 75 percent.

Choices: A 555 IC circuit is available. A capacitor with a value of

C = 1nF

is also

available.

Solution: The frequency of oscillation, as given by Equation (15.102), is

f =

0.693(R

+2R

Therefore,

+2R

(0.693) fC

(0.693)(50 × 10

)(1 × 10

−9

)

⇒ 28.9k

(15.104)

The duty cycle, given by Equation (15.103), is

Duty cycle = 0.75 =

+ R

+2R

which yields

= 2R

(15.105)

Combining Equations (15.104) and (15.105), we ﬁnd that

= 14.5k and R

= 7.23 k

nea80644_ch15_1061-1140.qxd 07/12/2009 3:58 Page 1106 pinnacle MHDQ-New:MHDQ134:MHDQ134-15:

Chapter 15 Applications and Design of Integrated Circuits 1107

Trade-offs: If standard-valued resistors are required, then

= 13 k

and

7.5k

would provide a frequency of 51.5 kHz and a duty cycle of 73.2 percent.

Comment: A wide range of oscillation frequencies can be obtained by changing the

resistance and capacitance values.

EXERCISE PROBLEM

Ex 15.11: The 555 IC is connected as an astable multivibrator. Let

= 20 k

= 80 k

, and

C = 0.01 μF

. Determine the frequency of oscillation and the

duty cycle. (Ans.

f = 802 Hz

, duty cycle

= 55.6%

)

Other Applications

When the 555 is connected in the monostable mode, an external signal applied to the

control voltage terminal will change the charging time of the timing capacitor and the

pulse width. If the one-shot is triggered with a continuous pulse train, the output

pulse width will be modulated by the external signal. This circuit is known as a pulse

width modulator (PWM).

A pulse position modulator can also be developed using the astable mode.

A modulating signal applied to the control voltage terminal will vary the pulse position,

which will be controlled by the modulating signal in a manner similar to the PWM.

Finally, a linear ramp generator can be constructed, again using the 555 mono-

stable mode. The normal charging pattern of the timing capacitor is exponential

because of the

circuit. If resistor

is replaced by a constant current source, a

linear ramp will be generated.

Test Your Understanding

TYU 15.10 (a) The Schmitt trigger oscillator is shown in Figure 15.35. The saturated

output voltages are

±5

V, and

= R

= 15



= 20



, and

= 0.05 μ

Determine the frequency of oscillation and the duty cycle. (b) Changing only the

value of

from part (a), determine the value of

such that the frequency of os-

cillation is

f = 1.2

kHz. (Ans. (a)

f = 454.5

Hz, 50% duty cycle; (b)

= 7.576

)

TYU 15.11 Consider the monostable multivibrator in Figure 15.37 with parameters:

= 8V

= 0.7

= 0.01 μF

= 10 k

= 20 k

, and

= 40 k

Determine the output pulse width and recovery time. (Ans.

T = 48.9 μs

= 37.8 μs

)

TYU 15.12 Design the 555 IC as an astable multivibrator to deliver a 1 kHz signal

with a 55 percent duty cycle. (Ans. For example,

C = 0.01 μF

= 14.43 k

= 64.9k

)

15.5 INTEGRATED CIRCUIT POWER AMPLIFIERS

Objective: • Analyze and design IC power ampliﬁers that usually con-

sist of high-gain small-signal ampliﬁers in cascade with an output stage.

Most IC power ampliﬁers consist of a high-gain small-signal ampliﬁer cascaded with

a class-AB output stage. Some IC power ampliﬁers are a ﬁxed-gain circuit with

nea80644_ch15_1061-1140.qxd 07/12/2009 3:58 Page 1107 pinnacle MHDQ-New:MHDQ134:MHDQ134-15: