CHAPTER 5

DIGITAL VOLTMETERS AND

FREQUENCY METERS

Digital voltmeters are essentially analog–to–digital converters with digital displays

to indicate the measured voltage. Digital multimeters are electronic volt–ohm–milliameters
with digital displays.
A digital frequency meter is a digital counter combined with an accurate timing
system. Conversely, an accurate frequency source combined with a digital counter
can be used for time measurements.

5.1 Digital Voltmeter Systems

5.1.1 Ramp–Type Digital Voltmeter

A digital voltmeter (DVM) essentially consists of an analog–to–digital converter, a
set of seven–segment numerical displays, and the necessary BCD–to–seven–segment
drivers. Fig. 5.1 illustrates the use of a ramp–type ADC as a digital voltmeter.
The counting circuitry, BCD–to–seven segment decoder/drivers, and digital read-
outs in Fig. 5.1 constitute a scale–of–2000 counter , and a latch is included in the
system. If the latch were not present, the digital readouts would be reset to zero at
the commencement of the counting time (t1 ), change rapidly as the count progresses
Measurements and Instrumentation, First Edition. 69
By Osama A. Alkishriwo Copyright c 2016 John Wiley & Sons, Inc.
70 DIGITAL VOLTMETERS AND FREQUENCY METERS

throughout t1 , and remain constant for t2 . Thus, the display would be virtually un-
readable. The latch circuits isolate the display from the counting circuits during
the time that counting is in progress. The positive–going edge of the comparator
output waveform at the end of the time t1 briefly triggers the latch to connect the
decoder/drivers to the counting circuits when counting has ceased. This corrects (or
updates) the display, if necessary, and otherwise allows it to remain constant and
readable. Latch circuits are basically special kinds of flip–flops

(a) DVM system. (b) DVM waveforms.

Figure 5.1 A ramp–type digital voltmeter (DVM).

Example 5-1
Calculate the maximum time t1 for the digital voltmeter in Fig. 5.1 if the clock
generator frequency is 1.5 MHz. Also, suggest a suitable frequency for the
ramp generator.

Solution
Maximum pulses counted, N = 2000
clock time period= f1

1 1
t1 = N× = 1999 ×
f 1.5 M Hz
= 1.33 ms
 DIGITAL VOLTMETER SYSTEMS 71

Select,

t2 = 0.25t1 = 0.25 × 1.33 ms

= 0.33 ms
t1 + t2 = 1.33 ms + 0.33 ms
= 1.66 ms

Ramp generator frequency

1 1
fR = =
t1 + t2 1.66 ms
= 600 Hz

5.1.2 Dual–Slope Integrator DVM

Ramp–type DVMs require precise ramp voltages and precise time periods, both of
which can be difficult to maintain. The dual–slope-integrator DVM virtually elimi-
nates these requirements by using a special type of ramp generator circuit (or inte-
grator). The integrator capacitor is first charged from the analog input voltage, and
then discharged at a constant rate to give a time period that is measured digitally.
The charge and discharge result in two (voltage versus time) slopes, which gives the
circuit its name dual–slope.
Consider the block diagram and waveforms for the dual–slope integrator DVM
illustrated in Fig. 5.2. During time t1 , the integrator capacitor is charged negatively
from Vi , giving a negative–going ramp, as illustrated. This produces a voltage (Vo )
that is directly proportional to Vi . The constant current source is then switched into
the circuit to discharge the capacitor, thus producing a positive–going ramp voltage.
The zero–crossing detector is a voltage comparator that gives a high (positive)
output when the integrator output waveform is negative, and a low output at the end
of the positive–going ramp (when the ramp voltage crosses the zero level). The AND
gate has high inputs from both the zero–crossing detector and the control waveform
only during the positive–going ramp time, that is, during time t2 . Pulses from the
clock generator pass through the AND gate to the counting circuits during this time.
The counting circuits are reset to zero by the positive–going edge of the control wave
(see dashed line) at the commencement of t2 , so the output of the counting circuits
is a digital measurement of time t2 . Since t2 is directly proportion to Vo , and Vo is
directly proportional to Vi , the output is a digital measurement of the analog input.

5.1.3 Accuracy

The accuracy of a digital multimeter depends on the type of measurement being

made; however, basic dc accuracy is usually ±0.7% of the reading, or better. Digital
instrument accuracy is usually stated as ±(0.5%rdg + 1d), or simply as (0.5 + 1).
This means ±(0.5% of the reading +1 digit), where the 1 digit refers to the extreme
72 DIGITAL VOLTMETERS AND FREQUENCY METERS

(a) System block diagram.

(b) System waveforms.

Figure 5.2 A dual–slope integrator DVM.

right (or least significant) numeral of the display. For an accuracy of (0.5 + 1), the
maximum error in a 1.800 V reading would be

error = ±[(0.5%of 1.8V ) + 0.001V ]

= ±0.01V
error = ±0.56% of the reading
 DIGITAL FREQUENCY METER 73

5.2 Digital Frequency Meter

The digital frequency meter illustrated in Fig. 5.3(a) consists of an accurate tim-
ing source (or time base), digital counting circuits, circuitry for shaping the input
waveform, and a circuit for gating the shaped waveform to the counter. The input is
first amplified or attenuated, as necessary, and then fed to the wave–shaping circuit,
which converts it into a square or pulse waveform with the same frequency as the
input [Fig. 5.3(b)]. The presence of this wave–shaping circuit means that the input
can be sinusoidal, square, triangular, or can have any other repetitive–type wave-
form. The shaped waveform is fed to one input terminal of a two–input AND gate,
and the other AND gate input is controlled by the Q output from a flip–flop. Conse-
quently, the pulses to be counted pass through the AND gate only when the flip–flop
Q terminal is high.
The flip–flop is controlled by the timing circuit, changing state each instant that
the timer output waveform goes in a negative direction (a negative–going edge).
When the timing circuit output frequency is 1 Hz, as illustrated, the flip–flop Q
output terminal is alternately high for a period of 1 s and low for 1 s. In this case,
the counting circuits are toggled (by the pulses from the wave–shaping circuit) for
a period (termed the gate time) of 1 s, and the total count indicates the frequency
directly in hertz. The counting circuits are reset to the zero–count condition by the
negative–going edge of the Q output from the flip–flop, so that the count always
starts from zero.
For the system illustrated in Fig. 5.3(a), the latch circuits are briefly triggered at
the end of the counting time by the positive-going edge of the flip–flop Q output.

(a) Frequency meter system. (b) System waveforms.

Figure 5.3 Basic block diagram and waveforms for a digital frequency meter.
74 DIGITAL VOLTMETERS AND FREQUENCY METERS

5.2.1 Range Changing

When a 1 s time period is used for counting the input pulses, the 3 12 digit display in
Fig. 5.3 might have a Hz unit identification alongside it, as illustrated. Alternatively,
as shown in Fig. 5.4(a), the frequency units could be identified as kHz if a decimal
point is included after the first numeral
Now consider the effect of using a 100 ms counting time instead of a 1 s time
period. A display of 1999 indicates 1999 cycles of input waveform per 100 ms, or
19.99 kHz [Fig. 5.4(b)]. Thus, when the time base is switched to 100 ms the dec-
imal point must also be switched. Similarly, if the time base is switched to 10 ms,
the decimal point is moved right once again, so that the maximum measurable fre-
quency is 199.9 kHz [Fig. 5.4(c)]. A further switch of the time base to a period of
1 ms gives a maximum pulse count of 1999 pulses per 1 ms, or 1.999 M Hz [Fig.
5.4(d)]. Fig. 5.4(e) shows a switching arrangement for the selection of time period
and decimal point.

Example 5-1
A digital frequency meter has a time base derived from a 1 M Hz clock gener-
ator frequency divided by decade counters. Determine the measured frequency
when a 1.512 kHz sine wave is applied and the time base uses (a) six decade
counters and (b) four decade counters.

Solution

(a) Using six decade counters:

Time base frequency, f1 = 1 M Hz
106 = 1 Hz
1
Time period, t1 = 1 Hz = 1 s
Cycles counted,

n1 = (input frequency) × t1
= 1.512 kHz × 1 s
= 1512 cycles

Measured frequency, f = 1.512 kHz

(b) Using four decade counters:
Time base frequency, f2 = 1 M Hz
104 = 100 Hz
1
Time period, t2 = 100 Hz = 10 ms
Cycles counted,

n2 = (input frequency) × t2
= 1.512 kHz × 10 ms
= 15 cycles

Measured frequency, f = 01.5 kHz

 DIGITAL FREQUENCY METER 75

(d)

(e) Selection of time period and decimal point.

Figure 5.4 Time period and decimal point selection for a digital frequency meter.

5.2.2 Frequency Meter Accuracy

The time base could switch the AND gate on or off while an input pulse (from the
wave–shaping circuit) is being applied. The partial pulses that get through the AND
gate may or may not succeed in triggering the counting circuits. So there is always
a possible gating error of ±1 cycle in the count during the timing period. This (one
count) is defined as the least significant digit (LSD). Thus, the accuracy of a digital
frequency meter is usually stated as

±1 LSD ± time base error

The total time base error might typically be < 1x10−6 , or less than 1 part in 106
parts.
76 DIGITAL VOLTMETERS AND FREQUENCY METERS

Example 5-2
A frequency counter with an accuracy of ±1 LSD ± (1 × 10−6 ) is employed
to measure frequencies of 100 Hz, 1 M Hz, and 100 M Hz. Calculate the
percentage measurement error in each case.
Solution
At f = 100 Hz

error = ±(1 count + 100 Hz × 10−6 )

= ±(1 count + 1 × 10−4 counts)
' 1 counts
 
1
% error = ± × 100%
100 Hz
= ±1%

At f = 1 M Hz

error = ±(1 count + 1 M Hz × 10−6 )

= ±(1 count + 1 count)
' 2 counts
 
2
% error = ± × 100%
1 M Hz
= ±2 × 10−4 %

At f = 100 M Hz

error = ±(1 count + 100 M Hz × 10−6 )

= ±(1 count + 100 count)
' 101
 counts 
101
% error = ± × 100%
100 M Hz
= ±1.01 × 10−4 %

PROBLEMS
5.1 Calculate the maximum measurement error for a digital voltmeter with an ac-
curacy of (0.1% rdg + 1 d), when indicating 1.490 V
5.2 A digital frequency meter uses a time base consisting of a 1 M Hz clock gen-
erator frequency–divided by six decade counters. Determine the meter indication
(a) when the input frequency is 5 kHz and the time base output is selected at the