March, 1949
91
Electronic Engineering
mproved Accuracy with a " Q" -Meter by the
Use of Auxiliary Components
A. C. LYNCH, M.A.*
The following method is useful
whether the specimen has high or
low loss. It uses the " Q "-meter
with an external galvanometer in
such a way that the errors (b) and
(c) are eliminated. The error (a)
can be avoided by the use of one
By
A" Q "-METER consists of an
oscillator with output control, a
resonant circuit with provision for
connecting specimen inductors or
capacitors, and a voltmeter calibrated in terms of " Q." The
general circuit is shown below the
dotted line in Fig. 1. It constitutes or, if necessary, two external capacia convenient piece of apparatus for tors. The only component in the
the rapid measurement of induct- " Q "-meter which is required to
rl
.
Ei
A reflecting galvanometer is also
required for the measurement of the
response in the resonant circuit, as
the built-in meter, while just
adequate when near full-scale,
cannot be read
accuracy at low
with sufficient
readings. The
additional meter (suitably shunted)
can be connected in series with the
ance or capacitance, and of the show any property other than internal meter.
Fig. I shows this arrangement.
associated resistive losses.
stability is the thermocouple, which
It is a matter of common experi- is assumed to maintain a voltage It involves no modification to the
ence that its accuracy, in measure- accurately proportional to the " Q "-meter other than the fitting
ments of losses, is not better than square of the current in its heater. of four terminals, two of which
about '20 per cent. This accuracy
require to he short-circuited for use
can be somewhat improved by using TheModified Circuit
of the " Q "-meter in the normal
the reactance -variation method of
The
principle
used
is
that
of
the
measurement-i.e., measuring the reactance -variation method.' For manner.
breadth of the resonance curveof Resistance or Conductmethod it is usual to maintain Calculation
but it is still only of the order of that
ance
a
constant
input
voltage
and
observe
5 to 10 per cent, especially when the
The total conductance of the
" Q " is low. The causes of these the resulting voltage as the circuit
is detuned-i.e., to obtain the resonant circuit is given by
errors include :
(a) inaccurate
calibration of resonance curve. The present prowAC
G
tuning capacitors (either errors posal is to increase the input voltage
2
V le -1
in calibration, or insufficient scale - in known ratios, and to find how
(the
meaning
of
the symbols can be
much the circuit must be detuned
reading accuracy);
calibration of to maintain a constant voltage in it. inferred from Fig. 2).
(b) inaccurate
It is convenient to write
voltmeter-i.e., of " Q " scale;
The input voltage is measured by
(c) coarseness of scale of volt- a thermocouple and galvanometer;
AC
S
-meter at low voltages.
to obtain the necessary reading
2\1 k' -1
It has also been suggested' that accuracy, a reflecting galvanometer
an external galvanometer, with is used, external to the " Q "-meter, so that for the ratios given by the
arrangements for backing off most and connected in parallel with the apparatus described below,
AC
of the current, should be used, in " Q -range " meter. The known
AC
and
S('lace of the built-in meter, in the ratios of input voltage are measured
2
3
voltmeter part of the " Q "-meter. by shunting this galvanometer and respectively, for the two
ratios proThis is satisfactory for measure- maintaining its deflexion constant.
vided.
ments on specimens of low loss.
The load on the thermocouple can
If measurements of S are made
be kept constant.
* Post Office Research Station, London, N.W.2.
with and without a specimen connected, and the difference in this
quantity is written as S., then for
Additional Terminals
to be Strapped for
Additional -Terminals
Normal Use -
Q-Ronge
I. (Left).
General
arrangement of " Q "
meter with
external
galvanometer
Fig.
Thermocouple
Voltage in
Resonant
Circuit
Er
Er
Typical
resonance
curve
to
illustrate meaning of
symbols (see text)
Fig.
2
(Right).
Terminals
for External
Capacitor
Capacitance
92
March, 1949
Electronic Engineering
a capacitive specimen, of capaci-
tance C.,
power factor
Ss
C.
;
X.
.*.
2550
980
4540
and for an inductive specimen, of
inductance L.,
capacitance C.,
resonating
with
Fig. 3.
so
Single galvanometer
circuit with detailed resistance values
Co
and series resistance of the specimen
= OL32Ss
so
Thermocouple
Terminals
wC.2
The specimen may be connected
in parallel with the original coil
rather than with the condenser;
capacitative specimens should be
connected in parallel with the
capacitor.
An Equipment on this Principle
A set of equipment has been con-
structed around a Boonton 160-A
" Q "-meter.
The thermocouple
galvanometer must give full-scale
deflexion for about 2 mV input; a
Cambridge reflecting galvanometer
of 560 ohms resistance has been used.
(This is an unnecessarily high resistance; about 50 ohms would probably
have been more suitable). This
Voltmeter
Terminals
wound resistor with a
radio -type resistor to
adjust to the required value
across either the coil or the capacitor
of the " Q "-meter, and the breadth
of tuning will be the same in each
case, provided that the resistance of
the
injector " resistor can be
ignored. But since " Q " is given
1
by
, where G is the total cir(oLG
cuit conductance and L the inductance between the " coil " terminals
of the " Q "-meter, the potential at
the voltmeter is greater when L is
small. As the measurement is easier
when the potential is larger, inductive specimens should be connected
Valve
4( These ore each a wire -
frequency varies when this control Tests of Accuracy of Measurement
is operated and the result is that
Three groups of tests have been
the resonance curve is slightly un- made :
symmetrical.
1. Measurements on resistors;
The breadth of the
curve is, however, unaffected.
these tests verify that the principle
As the fine tuning capacitor of is sound and that the resonance
the " Q "-meter has an inaccurate curve is being correctly measured.
2. Measurements, at the lowest
calibration, and is not always of
sufficient range, while the main tun- convenient frequency, on a capaof very low power factor; these
ing capacitor cannot be read to citor
measure
the conductance of the
better than 1 ti/LF in some parts of
tuning
capacitor
in the " Q "-meter.
its scale, an external capacitor is
3.
Measurements,
at a high freneeded.
A Muirhead Type 11-1) quency, on capacitors
separately
capacitor of 70 NT range and 0.008 and together;
these measure the
AiLF per scale division is used; it is series resistance of the tuning capanot ideal-in some respects it is of citor in the " Q "-meter.
unnecessarily good quality, and on Tests with Resistors
the other hand, its minimum capaThe resistances of a number of
citance of about 30 AiLF is objecsurface -type carbon resistors were
tionably large-but it is probably measured
in a D.C. Wheatstone
the most suitable component combridge and also at I Mc/ s. and
mercially available.
Me / s. in the apparatus described.
The stability of this " Q "-meter, 10
Discrepancies in the 10 Mc / s.
though adequate for normal use, is measurements were found to be due
not sufficient for the present purpose unless its power supply is to the inductance of the external
capacitor and the leads to it. The
obtained through a constant -volt, apparent capacitance is:age transformer.
C1(1 + W2L,C),
After a little practice, it is pos- where Ci is the low -frequency
galvanometer requires about 5,000 sible to make a set of measurements, capacitance, and L the
ohms external resistance for critical on one resonance curve, in n to 2 ance, of the capacitor inductand its
damping. The switching of the cir- minutes.
leads; since C. is itself variable, the
cuit is arranged to give ratios of
input voltage of 1: V2 : V 3.25; it
Table
maintains both a constant load on
Resistance at 10 Mc s.
the thermocouple and nearly critical
Resistance Resistance
I
clamping
of
the
galvanometer.
at D.C.
at
--
Mc/s.
1
Details are shown in Fig. 3.
C,-50 i.,./t1r
82
F
1 14µµF
correction
for
The same galvanometer can be
used for the resonant -voltage readings, by additional switching as
shown. The shunts are arranged so
that, in the least sensitive position,
full-scale deflection corresponds to
a " Q " of about 200.
The control of oscillator output
in this " Q "-meter is carried out by
variation of the H.T. voltage. The
C,-82Nl,F.
without
inductance
Megohms
2.72
1.562
570
268
119.4
Thousands of ohms
2.90
1.57
560
28,
124
67.7
33.0
67.
33.
17.76
16.,
10.01
5.89
2.72
122
270
122
33.,
65.,
33.;
31,
108.,
33.,
75.,
38.,
10.0,
19.,
11.7
17.1
10.0,
10.10
5.7,
2.6,
141
6.6,
3.0,
March, 1949
93
Electronic Engineering
Table 2
correcting.factor for S is :-
10 Mc / s., and was found to be 0.24
Some of the measurements
were then repeated with different
settings of the external capacitor,
All.
(10 megohm
( I megohm
(100,000 ohm
...
Capacitor, 100 Auf
...
...
...
...
Resistor
Accuracy
Quantity measured
Frequency
Type of impedor
(1 + 2,02LiC,1).
The inductance Li was deduced
from measurements of capacitance at 200 Kc/s. and at
100 KC/s.)
I
Mc/s.)
10 Mc/s.)
any
Resistance
2%
Power factor
0.00003,
Series resistance
0.001
or 1%,
whichever is
larger
Inductor, 40/./H
I
Mc/s.
and consistent results were obtained
as shown in Table 1.
specimen would therefore appear to
The correction for inductance is be less when the capacitor was set
thus very important at 11 'Mc/ s. At at a high value. The observed
20 Mc / s., with Ci = 50 API', it results show that no change in
amounts to 40 per cent, and there-
caused
by
losses
ohm, or 1%,
whichever is
larger
in
auxiliary
apparatus-e.g., in the external
capacitor which would be needed to
resonate with the inductor in the
of this type exceeds the error in last example given. The method is
fore sets the upper limit of frequency measurement, which is about 0.02 therefore as good as, but no better
usable. At 2 Mc / s. it is 1 per cent, ttAF; the series resistance of the con- than, any which involves comand above this frequency the cor- denser is therefore less than 0.01 ponents of normal laboratory types.
rection should normally be applied. ohm.
The next step in improving the
accuracy and convenience of workTests with a Capacitor of Low Power - Summary of Possibilities
Factor
A " Q "-meter used as described,
A capacitor was formed of two with
an external galvanometer and
stainless -steel plates, 4 in. square, variable capacitor, can be used to
separated by three freshly -cut frag- measure resistive components of
ments of Distrene, of about 1 mm. impedances (whether the impedance
If
ing,
using this principle of reac-
tance -variation with constant response, would be to obtain the
various input voltages from a capacitive potentiometer of known
ratios;
this would eliminate the need
thickness.
is mainly resistive, inductive, or
Several measurements were made, capacitive) in the frequency range for the thermocouple. Experience
described has
all at 150 Kc / s., with each of two 100 Kc/s. to 20 Mc/ s. The accuracy with the equipment
in any such further
shown
that
tuning coils. The results were :
of the measurement of S, a quantity development, the greatest care must
defining the breadth of the resonance be taken to minimise stray inducCapacitance of"Q"-meter Decrease of S on
connecting
tuning capacitor
curve, is limited to about ±0.0003 tance.
" specimen "
titIF by instability of oscillator
with
scale divisions°
without
"specimen "" specimen "
frequency and of the capacitance of Acknowledgments
p.f.tF
(I div..--0.008µµF)
,ut5F
various components, and to about
The experimental work described
392
I, O.5. 0.5, 0,
305
1.5
±1 per cent by instability of the was carried out at the Post Office
and the scale -reading Engineering Research Station by
accuracy of the galvanometer. This the author and Miss S. Rodwell, and
Hence the change of conductance of quantity S is equal to G/6), where is published by permission of the
the capacitor is of the order of G is the conductance of the circuit. Engineer -in -Chief of the Post Office.
0.004 micromho for 87 AA?, and its This accuracy corresponds, for
example, to each of the following : References
power factor about 0.00004.
-0.5, 0.0, 0.5, 1.,
75
162
voltmeter
The full accuracy thus calculated
Tests with Capacitors Separately and cannot
Together
always be obtained in
measurements on capacitors and
Two silvered -mica capacitors, A inductors, as there will be errors
and 13, were measured separately and
also in parallel at 10 Mc/ s. When
in parallel they had separate leads
to the " Q "-meter terminals.
The results were :
Capacitance of Increase of S
Q -meter tuning on connecting
B
capacitor
(two
without with
determina"B" "B
tions)
con-
con-
nected netted
NuF
" A " not connected
" A " connected
379
302
0.05,,
0.11
148
71
0.065,
0.06
tf there were resistance in series
with the tuning capacitor, the con 41
lance or the capacitor would
vary with setting, the variation
Icing more rapid at the higher capaita,nces.
The conductance of a
1 P. H. Mead, in a Report by R.A.E., Farnborough, not generally available.
2 See, for example, Hartshorn and Ward,
J.I.E.E., 79, p. 597 (1936).
The New Secretary of :
The Department of Scientific and Industrial Research
Sir Edward Appleton, K.B.E., Civil Service and has risen from the
K.C.B., will relinquish on April 30, lowest grade.
Previous holders of the appoint1949, his appointment as secretary
to the Committee of the Privy ment are :Frank
Heath,
1916-1927-Sir
Council for Scientific and Industrial
G.B.E., K.C.B.
Research.
1927-1929-Sir
Henry Tizard,
The King has been graciously
G.C.B.,
A.F.C., F.R.S.
pleased to approve the appointment
Frank
1929-1939- Sir
Smith,
of Sir Ben Lockspeiser, M.A.,
G.C.B.,
G.B.E.,
F.R.S.
M.I.Mech.E., F.R.A.S., to succeed
1939-1949-Sir Edward Appleton,
Sir Edward Appleton.
G.B.E., K.C.B., F.R.S.
Sir Ben Lockspeiser is at present
Sir Ben Lockspeiser will be 58 this
chief scientist at the Ministry of year. He was a scholar at the
Supply and will take up his new Sidney Sussex College, Cambridge,
appointment on May 1, 1949.
where he took Natural and MechaniHe is a member of the Scientific cal Sciences with honours.