6. Radio Frequency Bridges: Part 3.
610. Practical Impedance Bridges:
In previous discussion, we established the basic principle that
an impedance bridge compares a known or reference impedance against
an unknown impedance. This implies that we need a calibrated variable
resistor, and also, somewhat less encouragingly, a calibrated
variable reactance that can vary smoothly from inductive to capacitive.
We might try to make such a device by placing a variable capacitor
in series with an inductor; except that the transition from capacitive
to inductive will vary horribly with frequency; and attaching
the word "reference" to the such a network is not the
activity of a sane and rational mind. Fortunately, the concept
of
conjugate reactance saves the day; i.e., if the
impedance
is capacitive, we can compare it against a resistor and a variable
capacitor in the obvious way; but if the impedance is inductive,
then we might use the variable capacitor to
cancel
the
inductance, and simply observe that the unknown reactance is
numerically
the same as that of the reference capacitor, but of opposite sign.
Even this is a little inconvenient however, because it involves
switching both terminals of the capacitor from one arm of the
bridge to the other, and so complicates arrangements for earthing
and balancing of straycapacitances. A better solution therefore,
is to connect the variable capacitor permanently into the reference
arm of the bridge, and insert a fixed
offset
capacitor
into the unknown arm.
Simple practical implementations of the transformer ratioarm
bridge (TRAB) shown above have appeared in various publications
(see refs [
6],[
24],[
30],[
31]).
The
variable reference resistor should be physically small and
noninductive,
e.g., a 1W Cermet (ceramic metalglaze) potentiometer. Resistance
measurements above about 500Ω are likely to be inaccurate,
and so 500Ω or less is a sensible choice for the resistance
value. Helical potentiometers are (regrettably) unsuitable due
to selfinductance, and wormgear adjusted straighttrack
potentiometers
are likely to suffer from backlash; and so a conventional 270°
potentiometer with a reduction drive is indicated. In this depiction,
specifications for the generator and the detector are omitted,
because we have the options of connecting a noise source to one
socket and a radio receiver to the other; or of connecting a signal
generator or an attenuated transmitter to the socket designated
as input and using a diode detector, or an oscilloscope, or an
RF millivoltmeter. We may also, incidentally, use a narrowbandwidth
generator and a radio receiver, thereby obtaining extreme sensitivity
(and immunity to harmonics in the generator output) in exchange
for having to tune the receiver to the generator frequency every
time a measurement is made. Note that there is no DC path through
the bridge at the socket labelled 'Det/Gen', and so an RF choke
or a resistor must be connected across this port if a halfwave
rectifier is to be used here. The bridge however is a linear reciprocal
network, and so a generator signal may be inserted at the 'Det/Gen'
socket, and a rectifier circuit connected at the 'Gen/Det' socket,
in which case a DC path
is available. In addition
to the
components shown, a terminating resistor is sometimes connected
across the generator so that it may work into a reasonably nonreactive
load.
In setting up this
bridge, C
offset is chosen (or
adjusted) so that the bridge
balances with C
Ref in the
centre of its
range when a (nearaspossible) pure resistance is connected in
place of the unknown impedance
Zx.
The capacitor dial is then calibrated with zero at the centre,
positive capacitance when C
Ref
is greater
than C
offset and negative
capacitance when
C
Ref is less than C
offset,
i.e., the dial is marked with the value of C
RefC
offset in pF. When the bridge is
balanced, the
reactive part of the impedance under test (
Zx=R
x+
jX
x) is given
by:
X
x = 1 / 2πf( C
Ref
 C
offset ).
where f is the frequency at which the test is conducted.
R
x is read directly from a
calibrated dial
attached to R
Ref.
Refs:
[
6]
The
ARRL Antenna Book,
19th edition, ARRL publ, 2000. ISBN: 0872598047.
A Noise Bridge for 1.8 through 30 MHz, Ch.27, p2431 [TRAB using
tonemodulated zenerdiode noise source and radio receiver as
detector. Transformer is wound on Amidon pignose (2hole) core
type BLN 432402, 3 turns primary, 3+3 turns secondary].
[
24]
The ARRL Handbook
2000, 77th edition. ARRL publ. 1999, ISBN: 0872591832.
A Noise Bridge for 1.8 through 30 MHz, Ch.26, p3638. Same as
[
6]
[
30]
"Tone Modulated
HF Impedance Bridge", E Chicken MBE, G3BIK. Rad Com,
June 1994 p1316, July 1994 p6970. TRAB using tonemodulated
zenerdiode noise source and radio receiver as detector. Frequency
range 130MHz. Transformer is wound on Amidon FT5043 toroid (0.5",
μ
i≈900), 8
turns primary (≈33μH),
16 turns centretapped secondary.
[
31]
"
Noise bridge
measurements", Brian Horsfall, G3GKG, Rad Com, April
2003, p6871. TRAB using zener noise source and radio receiver
as detector. Transformer is the same as in [
6]
Ch.27, p2431.
Couples to receiver using transformer (Amidon FT3777, 5:5 turns)
to float the unknown from earth. Obtains 9:1 scale expansion by
coupling reference resistor via a 3:1 autotransformer (FT3777
12 turns tapped at 4).
The main advantage of
using transformer
ratioarms has been mentioned before, i.e., sockets for the generator,
the detector, and the unknown impedance can all have one side
grounded to the chassis. There are disadvantages to the overall
bridge configuration however, as evidenced by inclusion of the
trimmer capacitors C
T1 and C
T2.
The problem is that there will be distributed stray capacitance
from all parts of the network to the chassis and to other parts
of the network. If one arm of the bridge has more stray capacitance
to ground than the other, some compensation is possible by increasing
either C
T1 or C
T2
from its minimum value; but there is no scheme that will compensate
for the stray capacitance across the reference resistor at all
settings of its dial. The result will be inaccuracy, which varies
according to the setting of the resistance dial and becomes more
and more serious as the frequency is increased. This is a major
drawback with the straightforward seriesequivalent impedance
bridge. The solution to the problem is to rearrange the components;
this time into a configuration known as an
admittance bridge.
611. Admittance Bridges:
The complex number representation of impedance,
Z=R+
jX,
makes it appear natural to compare an unknown impedance against
a series combination of resistance and reactance and so obtain
an expression for the impedance (almost) directly. It is however,
perfectly possible to compare an impedance against a resistance
and a reactance in
parallel, and then perform a
mathematical
transformation in order to obtain the seriesequivalent. The
disadvantage
is that additional calculation is required, but this is a small
price to pay for the advantage of the approach, which is that
it is possible to achieve nearcomplete compensation for the effects
of stray capacitance. There is moreover, no need to use an offset
capacitor, because all reference components can be grounded at
one end, and so the variable capacitor can be switched from one
arm of the bridge to the other without introducing balancing errors.
In setting up this bridge, a nearpure resistance (with very short
leads) is connected in place of the unknown impedance, and the
selector switch is set to X=0. The bridge is then balanced by
adjusting R
Ref and increasing
either C
T1 or C
T2 from its minimum
setting. This operation, which should be carried out at the high
end of the intended frequency range, cancels all of the circuit
stray capacitances; the only exception being that it cannot compensate
for any variation in the selfcapacitance or inductance of R
Ref which may occur as its dial is
rotated (although
such variation will have minimal effect if it is small in comparison
to C
min). The bridge is then
switched to
the X+ or X position, and the trimmer C
min
is used to obtain balance with C
Ref
set
to its nominal zero position. It is, incidentally, a good idea
to choose the zero position of C
Ref
to
be a little away from the endstop; firstly because variable capacitors
exhibit severe scale nonlinearity at the minimum capacitance
end, and secondly to give a little overlap between the X+ (inductive)
and X (capacitive) ranges as an aid when searching for nulls
around X=0. Calibration of C
Ref
can be
accomplished either by measuring it with an accurate capacitance
meter, of by placing known capacitors across the resistor attached
to the measurement terminals.
In use, when
measuring an inductive
reactance (X+), the reference capacitor scale indicates parallel
equivalent negative capacitance. This can be converted to parallel
inductive reactance using X
p=+1/(2πfC),
where f is the measurement frequency, and C (in this case) is
the capacitance dial reading. When measuring a capacitive impedance
(X), of course, the parallel equivalent reactive component is
X
p=1/(2πfC).
For a simple practical
implementation
of an admittance bridge see refs [
32ad].
Interpretation
of the information it provides is discussed next.
Refs:
[
32a]
"
A Simple and
Accurate Admittance Bridge", Wilfred N Caron, Communications
Quarterly, Summer (July) 1992, p4450.
Admittance TRAB for 230MHz using Amidon BLN 43202 twohole core
(A
L=2.89μH/turn²)
with singleturn
RG174U Faraday shielded primary and 3turn twisted bifilar secondary.
Calibration procedure using deliberately misterminated coax cable.
[
32b]
Forrest Gehrke, K2BT,
Communications Quarterly (Correspondence), Winter (Jan) 1993,
p9293.
Zenner noise source for the bridge. Advantages and limitations
of the transmissionline transformer approach.
[
32c]
"RF Impedance
Bridge for 230MHz", Jack Gentle, G0RVN, Rad Com July,
1995 p3842.
Article based on ref [
32a],
above. Transformer ratioarm admittance bridge.
Erratum: Transformer core is given as: "BLN 432023";
this should read: 'BLN43202'.
[
32d]
"Capacitor
Calibration
for the RF ZBridge", Jack Gentle, G0RVN, Rad Com, Aug1995
p61 & 63.
The admittance bridge furnishes us with two quantities, X
p and R
p;
i.e., it gives
us a resistance and a reactance that, when placed in parallel,
have the same impedance as the twoterminal network under test.
We may convert these measurements into the ordinary seriesequivalent
form, i.e.,
Z=R+
jX, by using the
parallelseries
transformation [
AC Theory, Section 18], i.e.:
Z =

Rp Xp² + j Xp Rp²
( Rp²
+ Xp² )


or:
R =

Rp Xp²
( Rp²
+ Xp² )

and

X =

Xp Rp²
( Rp²
+ Xp² )

The subject of Admittance was introduced in [
AC Theory,
Section
44]. The reason why the bridge is called an admittance bridge
becomes apparent if we invert the impedance expression from which
the parallelseries transformation is derived, i.e., since
Z=R
p×
jX
p/(R
p+
jX
p), we may
write:
Y = ( R
p +
jX
p
) /
j R
p
X
p
Now 1/
j=
j. Therefore:
Y = (
jR
p
+X
p)
/ R
p X
p
i.e. (using Hartshorn's definition for admittance [
33]):
Y = G + jB
= (1/Rp) j/Xp 
Hence
Conductance 
G = 1/Rp 
Susceptance 
B = 1/Xp 
Ref:
[
33]
RadioFrequency Measurements
by Bridge and Resonance Methods, L. Hartshorn (Principal
Scientific
Officer, British National Physical Laboratory), Chapman &
Hall, 1940 (Vol. X of "Monographs on Electrical Engineering",
ed. H P Young). 3rd imp. 1942.
Ch. I, section 3: Defines Admittance as
Y=G+
jB,
hence B
L=1/ωL and B
C=ωC.
The parallel equivalent resistance and reactance are simply the
reciprocals of conductance and susceptance (with appropriately
chosen sign). The admittance bridge therefore reads conductance
and susceptance almost directly. Consequently, the dial of the
reference potentiometer can be labelled "G" and calibrated
directly in milliSiemens (if so desired), i.e.:
RP
/Ω 
0

50

100

150

200

250

300

350

400

450

500

G /mS 
∞

20

10

6.67

5

4

3.33

2.86

2.5

2.22

2

The reference capacitor must still be calibrated in pF, but the
X+ (inductive) switch position may be marked "B=2πfC"
and the X (capacitive) position may be marked "B=+2πfC".
612. Negative Conductance, DC bias, and the universal bridge:
In an admittance bridge, any number of elements can be connected
in parallel in the current and voltage arms of the bridge. This
feature allows us to cancel the inductance of a device under test
and thereby measure it as a negative susceptance. It also allows
us to move the nominal zero position of the reference capacitor
away from actual zero (which can never be reached) by placing
a capacitor (C
min) across the
opposite
arm. What is perhaps a little less obvious, is that we are at
liberty to perform the same trick with the reference resistor,
i.e., we can move the nominal zeroconductance position of the
dial away from infinite resistance (which can never be reached)
by placing another resistor across the opposite arm. This facility
allows us to search for nulls around zero conductance, and thereby
measure devices that are almostpure reactances, i.e., capacitors
and highQ coils. With this final refinement, the transformer
ratioarm bridge matures into a generalpurpose instrument capable
of measuring resistance, reactance, capacitance, inductance, impedance,
admittance, conductance, susceptance; and, taking versatility
well beyond its logical conclusion, we can swap the reference
and the zeroing resistors, and measure
negative
resistance
and conductance.
Some readers, of
course, may be
aware that in the world of passive components negative resistors
are hard to find. In the late 1950s however, before anyone knew
how to make decent transistors, there was considerable interest
in the fact that some semiconductor devices have regions in their
characteristic curves where the current falls as the voltage is
increased. The archetypical device in this class is the Esaki
diode or
Tunnel diode (which we have met before in
the
guise of the back diode), which can be used to make fast trigger
devices and oscillators that work at microwave frequencies [
12],[
23],[
34].
The Esaki diode has now largely fallen out of favour; but as a
baptism by fire for engineering students, it is difficult to surpass
practical experiments involving the characterisation of
negativeresistance
devices using bridges that can measure negative conductance. We
include this information because the feature will be found in
oldbutgood RF bridges that can be obtained secondhand for very
little money. Such bridges must also have a DC bias facility,
which is necessary because negative resistance only appears on
critical adjustment of device standing current; but this feature
is also useful for characterisation of electrolytic capacitors
and the effect of static core magnetisation on the inductance
of chokes and transformers.
References:
[
12]
The Art of Electronics,
Paul Horowitz [W1HFA] and Winfield Hill, 2nd edition 1989, Cambridge
University Press. ISBN 0521370957.
Tunnel (Esaki) diode p1415, & p1060. Back diode p891, 893.
[
23]
Amplifier Handbook,
Ed. Richard F Shea. McGraw Hill, 1965.
Ch 12: Tunnel Diodes and Backward Diodes. Chang S Kim and Jerome
J Tiemann.
[
34]
Physical Electronics,
C L Hemenway, R W Henry, M Caulton, Wiley & Sons, New York,
2nd edn. 1967. LCCN. 6723327. Section 14.6: The tunnel diode,
p290294.
The circuit for a
'universal' laboratory
RF bridge is shown below. Here however we deviate from convention,
by drawing the circuit diagram in a way that renders it comprehensible.
This circuit is based loosely on the 1963vintage Hatfield Instruments
LE300A/1 RF admittance bridge [
Handbook ref], for no
better
reason than that the author happens to own one. The ratio arms
of this bridge are formed by two transformers, an isolating transformer
with primaries tapped at 1+1 and 10+10 turns, and an autotransformer
that further divides the 1+1 tappings by 10:1. Range switches
enable the reference and zeroing elements to be connected to the
different ratioarm taps in order to multiply their influences
on the balance condition by 10, 1 or 0.1. In this way, a capacitor
of say 250pF can also be used for measurements of 0 to ±25pF
and 0 to ±2500pF, and a resistor of say 500Ω can
also be used for measurements of 0 to ±50Ω and 0
to ±5KΩ. The influence of the unknown impedance Z
x can also be multiplied or divided
in the same
way, to provide a large selection of measurement ranges (including
a remarkable 0 to 2.5pF range); but best accuracy is always obtained
when the unknown and the reference components are all set to the
same multiplier. DC bias is introduced via a balun transformer
with its output in series with the generator, and the reference
and zeroing resistors are provided with large series DCblocking
capacitors to ensure that bias current only flows in the device
under test. Various trimmer capacitors used for nullingout stray
capacitances have been ommitted for clarity. The transformers
can all be wound on highpermeability ferrite beads (e.g., Amidon
FT5043). In the original, the secondary of the ratiotransformer
(connected to the generator socket) was 27 turns, and the generator
input transformer ratio was 33:11. These transformers are suitable
for a generator level of between 100mV and several volts (e.g.,
a standard lab. signal generator or the transverter output of
an HF transceiver), with a shortwave radio receiver as the detector.
The author's bridge incidentally came with a builtin
crystalcontrolled
generator and tuned detector operating on 1.591549MHz. This standard
measuring frequency is 10
^{7} radians/sec, i.e.,
2πf=10
^{7},
a choice that greatly simplifies reactance calculations and corresponds
very closely to the lowfrequency end of the shortwave spectrum
(the mediumwave band ends at 1.6MHz). The manual also states
that the bridge can be used up to about 15MHz with an external
generator and detector, but in reality, the internal layout is
rather expansive and the unit is somewhat inaccurate above about
5MHz.
How to calibrate the
universal bridge
becomes obvious when the variable resistors are considered as
conductances, i.e.:
G
ref = 1/R
ref
and
G
min = 1/R
max
If the reference resistor is rotated to its maximum resistance
position, the conductance will not be zero. Also, it is not desirable
to have the maximum resistance position at the endstop, because
there may be a resistance step or nonlinearity as the wiper moves
to the end of the track. The dial is therefore marked zero a little
away from the endstop, and the resistance at the chosen position
is measured and designated R
max.
The conductance
of the unknown impedance is then given by:
G
x = G
ref
 G
min
i.e.,
G
x = (1/R
ref)

(1/R
max)
The quantity G
refG
min
is marked on the "G" dial, and calibration is established
prior to each measurement by setting the "G" dial at
zero and adjusting the "Set zero G" resistor until the
bridge balances. This calibration step also involves simultaneously
setting the "C" dial to zero, and adjusting the "Set
zero C" capacitor. For best results, the bridge is rezeroed
after every change of range or frequency.
Hatfield LE300 A/1 RF admittance bridge.
Gives
direct readout
in μH and pF when operated with internal 10^{7}
radian/sec
(1.591549MHz) generator and detector.
3termina measurement and lowimpedance adapter
[xx]
Hickman's Analog and RF circuits, Ian Hickman.
Newnes
1998. ISBN 0 7506 3742 0. p182
The TRAB, Ian Hickman, EW+WW, Aug. 1994, p670672.
613. Vector and Scalar Addition:
In the AC bridge circuits discussed so far, a voltage detector
is used to sample the difference between two points in a network.
Because the voltages involved contain phase information, the quantity
sampled is a vector sum; and the two voltages are not equal unless
they are identical in both magnitude and phase. In some situations
however, we wish to ignore the phase information and sample only
the magnitudes of the voltages to be compared.
In the context of
vectors or phasors,
quantities that can be represented by magnitude alone are known
as
scalars, and the addition or subtraction of such
quantities
is known as
scalar addition. It so happens that the
diode
detector, by virtue of the smoothing capacitor, removes phase
information; which means that scalar voltage addition can be performed
provided that the voltages are rectified and smoothed before they
are compared. Later on, we will use scalar addition in the design
of resistance and conductance bridges that are immune to (i.e.,
ignore) reactance; but here we will establish the principle by
using it to develop a bridge that simply measures impedance magnitude,
i.e., 
Z.
614. Impedance Magnitude Bridge:
So far we have discussed bridges that represent impedance in its
normal R+
jX form, and in its reciprocal (admittance)
form.
There is, of course, another way of representing impedance, which
is in terms of
magnitude and
phase,
this being known
as the
polar form. Bridges that can indicate phase
while
ignoring magnitude will be discussed in
a
later section. A bridge that indicates magnitude but
ignores
phase is shown below:
In this bridge, R
0 and
ZX
share a common current
I, and so
VX=
IZX and
V0=
IR
0. These voltages, of course, contain
phase
information, and so if we subtract them directly, they only sum
to zero when R
0 and
ZX
are identical, i.e., when
ZX
is
real. After rectification and smoothing however, all phase information
is lost and we obtain:
V
1 = (√2) 
VX
 V
f1
= (√2)

I 
ZX
 V
f1
V
2 = (√2) 
V0
 V
f2
= (√2)

I R
0  V
f2
where V
f1
and V
f2
are the forward voltage
drops of their respective diodes.
Balance occurs when V
1=V
2;
in which case, since both detector loads are identical, the forward
voltage drop in D
1 will be
the same as
that in D
2 (provided that the
diodes are
reasonably well matched), and so R
0=
ZX.
Best sensitivity is
obtained when
the detector input resistance (≈R
D/2)
is larger than R
0 , but the
bridge will
still balance correctly if it is not because the nonlinearities
of the two diodes will tend to cancel. For measuring impedance
magnitudes of up to about 1KΩ, at frequencies above about
100KHz; R
D can be in the
range 1 to 10KΩ,
and C
D about 0.1μF. A
suitable choice
of meter is 50050μA, with a 100KΩ sensitivity
control.
A property of this bridge that should be noted incidentally, is
that it is not a linear reciprocal network, i.e., there is no
definable detector port into which an RF signal can be injected.
Notice also that it does not have ratio arms; it works instead
by passing the same current through two impedances and comparing
the magnitudes of the voltages across them.
One particularly
useful feature
of the 
Z bridge, and of magnitude bridges in
general,
is that balance is monitored by means of a centrezero indicator.
This means that that the bridge output contains information regarding
the direction in which R
0
should be adjusted;
which is both convenient for manually operated bridges, and serves
as a basis for providing an input to a DC servo amplifier in a
selfadjusting system. In order to make the bridge output suitable
for driving a servo amplifier however, it is sensible to alter
the configuration to that shown below:
In this case, the diode D
2
has been reversed.
This means that at balance, the two output voltages V
1
and V
2 are now equal and
opposite,
and the voltage at the junction of the two equal summing resistors
(R
s) is zero. If 
ZX
is larger than R
0, the input
to the amplifier
goes positive, and vice versa; and the output of the amplifier
can be used to drive a motor, or a voltmeter, or both. In order
to avoid loading the detectors, the summing resistors should be
at least ten times larger in value than R
D,
but since the servo amplifier is likely to be based on an operational
amplifier with a high input impedance, this is not a problem.
In the diagram incidentally, the motor is shown ganged to R
0, but it could equally well be
ganged to some
mechanism that alters the magnitude of
ZX,
thereby forming part of an automatic impedance matching system.
In the pursuit of
automation, the
interesting property of an impedance magnitude bridge is that
its output is a proper measure of the effect of a transformer
in a power transmission system. We noted in [
AC Theory, 41],
that if an ideal transformer has its secondary winding loaded
with an impedance
Z, the impedance
Z'
looking into
the primary winding is given by:
i.e., a transformer scales the
magnitude of an
impedance without affecting the phase angle (to a first approximation
at least). We may therefore conceive of an antenna matching system
that uses a switchable or variable transformer to obtain a particular
value of impedance magnitude (e.g., 
Z'=50Ω),
and
a conjugate reactance to bring the phase angle to 0°. These
adjustments, in combination with magnitude and phase bridges that
give bidirectional voltage outputs, form one possible basis for
an automatic antenna tuning system (see [
AC Theory, 42 and
43] ). In order to pursue such ideas further however, we need
to devise bridges that can measure impedance related quantities
without interfering significantly with the power transmission
process.
615. Monitoring Bridges:
In most of the bridges discussed so far, the object of the exercise
has been to measure impedance by comparing it against one or more
variable reference elements. In antenna matching applications
however, it is normal for the bridge ratio to be fixed, and for
balance to be achieved by adjusting the load impedance. In this
situation, the bridge becomes a monitoring device, i.e., a box
of tricks to be inserted in the line between the transmitter and
the antenna or matching unit, and it is advantageous to design
it in such a way that it absorbs minimal energy from the signals
passing through it. Using Christie's circuit (or some AC variant
of it) this can be done by reducing the resistance in the
currentsampling
(reference) arm, and adjusting the ratio arms accordingly, and
so our prototype is the arrangement shown below:
The ratio arms (
Z1
and
Z2)
can be resistors, capacitors, or a transformer.
Note that the load impedance, being usually an antenna system
with a matching network, will probably not have handy controls
for independent adjustment of resistance and reactance; but these
quantities can nevertheless be manipulated in some way or another.
At this point also, we will adopt a consistent notation:
Vv for the voltage analog, and
Vi for the current analog; and we will
start
to ignore a redundant property of Christie's bridge, which is
that balancing
Vv
against
Vi
is the same as balancing the voltage across
Z2
against
the voltage across the
load. If one condition is satisfied, then the other is automatically
satisfied, and there is no need to consider them both. For an
impedance monitoring bridge, the component values are chosen so
that
Vv=
Vi
when the load impedance is equal to the target load impedance,
i.e., if the target load impedance is designated R
0:
Vv =
V
Z1
/ (
Z1 +
Z2)
=
Vi =
V
R
ii
/ ( R
ii + R
0
)
which, after rearrangement, gives the balance condition:
The symbol 'R
0' for the
target
load resistance is, incidentally, chosen deliberately to be the
same as that for the characteristic resistance of a transmission
line; R
0 being inevitably the
characteristic
resistance of the coaxial cable into which the monitoring bridge
is inserted. R
0 is now, in a
sense, the
characteristic resistance of the bridge.
If the target load
impedance is
50Ω, we will presume for now (somewhat unrealistically)
that there will be no great difficulty in designing a voltage
sampling network (
Z1+
Z2) that has a reasonably high
impedance relative
to it. We need to develop a reasonable voltage across the current
sampling resistor R
ii
however, and this
implies that there will be a voltage drop in the line resulting
from the insertion of the bridge. If we decide that the maximum
acceptable voltage drop is (say) 1% (0.09dB), then R
ii
must be no greater than 0.5Ω, and even at a power level
of 100W, 
Vi
will only be about
0.7V RMS. This is too low to give good linearity with a simple
diode detector, and although we might decide to compensate for
the nonlinearity, or increase the signal by using amplifiers,
we should observe that there is more than enough power available
to work a 100μA meter; and we should not be forced to use
circuits
that need batteries or a mains power supply. The solution is to
replace the current sampling element with a stepup transformer;
as in the prototype circuit shown below:
The transformer makes it possible to increase 
Vi
to a level suitable for a diode detector, or alternatively, it
allows the insertion loss (i.e., the power consumed by the current
sampling element) to be reduced to a very low level if a low output
voltage is acceptable. It also has the significant advantage that
it allows the voltage analog
Vv
and the detector to be referenced to ground; which means that
we have the option of dispensing with the diode detector and bringing
that end of the transformer to a coax socket. We are then in a
position to exploit the fact that the bridge is a linear reciprocal
network by injecting a signal of a few tens of milliVolts into
the 'detector' port and adjusting the antenna impedance for minimum
response at a receiver (i.e., a transceiver switched to receive)
connected in place of the generator. In this way, an antenna can
be matched ready for transmission without radiating a detectable
carrier; the procedure being known as "quiet tuning"
[
35],[
36] or, perhaps more
evocatively, "stealth
tuning".
Refs:
[
35]
Simple Quiet Tuning
and Matching of Antennas M. J. Underhill G3LHZ, Rad Com, May
1981, p420422.
The antenna can be matched in receive mode by injecting a small
signal into a reverse wave directional coupler in the line to
the ATU. The antenna is matched when the level of injected signal
heard in the receiver is minimised. The injected signal can be
from a noise source, or it can be a combspectrum from, say, a
crystal calibrator. The injected signal is too weak to interfere
with other stations, being undetectable at about 1 wavelength
from the antenna.
[
36]
A Quiet Antenna Tuner,
Tony Lymer GM0DHD, QEX May/June 2002, p912.
UnderhillLewis method. QRP singlecore version of SontheimerFredrick,
performs well from 1.8  146MHz.
The bridge now looks
very different
from Christie's circuit; but the basic principle of operation
(the comparison of a voltage analog and a current analog) is the
same once the properties of the transformer have been taken into
account. Differences to note are that there are now only two voltages,
Vv and
Vi,
to be reconciled (the previously mentioned redundancy has disappeared),
and we now have additional parameters; particularly, the transformer
turns ratio and the secondary load resistor R
i,
which play a part in determining the balance condition. For this
reason,
Z1
and
Z2
are no longer solely responsible for determining the ratio between
the current and voltage samples, and should no longer be described
as ratio arms. Instead,
Z1
and
Z2
form a
voltage sampling network,
and the transformer and its secondary load form a
current
sampling network. A transformer in this application
is
called a
current transformer,
and as we shall see
in the next section, the resistor R
i
that
shunts the secondary is essential for the production of an output
voltage proportional to and approximately in phase with the current.
© D W Knight 2007.
David Knight asserts the right to be
recognised
as the author of this work.
Further Work
Topics that perhaps ought to be added:
A. Table of
common bridge types + a few more obscure ones
B. Obtaining
information from outof balance bridges.
C. Complex
Z
measurement using only
scalar voltage
measurements.
Strandlund, QST, June 1965, p2428.
Gruchalla, CQ, Fall 1998, p3343
The
MFJ 269 antenna
analyser (for example), uses scalar
addition
of voltages from a simple symmetric resistor ratioarm bridge.
Despite the alarming lack of quantitative information in the manual
on the subject of instrumental accuracy; the author's MFJ269
gives good inductance measurements. Readings in the region of
10 μH at the lowest working frequency (1.7 MHz) agree within
2% with measurements made using a Hatfield LE300/A1 at 1.5915 MHz
(error ±0.5%).
The facility for
capacitance measurement
appears somewhat crude by comparison: readout is to the nearest
pF and error is about 10% in the region of 100 pF; but this limitation
can be worked around with the aid of a calculator. The trick is
to use the displayed reactances and subtract an offset for the
jig capacitance, all of which can be done using readings from
the instrument itself. It is possible in this way to measure small
capacitances to about 1 decimal place in pF, making the MFJ269
useful in the lab. as well as when fettling antennas.