RadioFrequency
Bridges
Their principles of operation and their relationship to the
WheatstoneChristie
prototype.
by David Knight
Introduction:
In this chapter we explore the subject of AC measuring and monitoring
bridges; particularly with a view to understanding how they work
and how to optimise them for use across the 1.6  30MHz HF radio
spectrum. In the course of the discussion we will show how to
devise bridges that can be used to make accurate measurements
of any impedancerelated quantity, including reflectioncoefficient,
impedance magnitude, resistance, conductance, and phase; thereby
covering the design considerations for SWR bridges, Match Meters,
and bridges for automatic antenna matching systems. Full comprehension
of the discussion to follow requires familiarity with the material
presented in chapters
1 to
5.
1. Christie's Bridge:
The term 'bridge' came into the language of electrical engineering
in connection with the "Wheatstone Bridge", which was
actually first described by Samuel Hunter Christie of the Royal
Military Academy in Woolwich in 1833. The bridge is usually attributed
incorrectly to Sir Charles Wheatstone, who employed it extensively
in his scientific experiments, although Wheatstone himself always
credited the bridge to Christie [
1]. The circuit is
so
called because the detector (a centrezero galvanometer, i.e.,
a microammeter or voltmeter) occupies the position of a bridge
between two potentialdivider networks. Two possible implementations
of Christie's bridge are shown below:
The bridge is balanced by adjusting a variable element
until the
voltage across the meter (and hence the current through it) is
zero. In the lefthand version, the variable element is a potentiometer
R
1+R
2,
traditionally
constructed by laying a length of resistance wire against a measuring
scale, and known as a 'slidewire' [introduced by Kirchhoff. See
Gray, Abs Meas E&M 1921, p340]. At balance the ratio R
1/R
2
is equal to R
0/R
x, where R
0
is a standard (i.e., a laboratory reference) resistor, and R
x is the unknown resistance under
test. In the
righthand version, the ratio R
1/R
2 is fixed, and R
0
is
a calibrated variable reference resistor. In this case, it is
quite common for R
1 to be
made equal to
R
2, because this situation
gives greatest
meter sensitivity and hence the best accuracy of measurement.
When R
1=R
2,
then
V
1=V
2,
and the bridge
balances when R
0=R
x.
There are various
ways of proving
the balance relationship R
1/R
2=R
0/R
x (see, for example,
ref [
2]), but here we are interested not so much in
measuring
resistors, as in generalising the bridge concept and showing that
all bridges are direct descendants of Christie's. We will begin
therefore by observing that the unknown resistor R
x
must obey Ohm's law, i.e.,V
x
= I
xR
x,
or:
Let us observe, for the moment, that we can determine
V
x if we need to because we
know that, at balance, V
x = V
2,
and V
2 can easily be
calculated if we know
the supply voltage V and the values of R
1
and R
2. To determine I
x
however, we need to sample the current flowing through the unknown
resistor; and we may do this by placing a resistor R
0
in series with it, and measuring the voltage V
0
that appears across R
0. Thus V
0
is directly proportional to I
x,
i.e., V
0=I
xR
0
and so:
I
x = V
0
/ R
0
If we now substitute this expression for I
x
into equation (
1.1)
above,
we obtain:
R
x = R
0
V
x
/ V
0
Now at balance, V
1=V
0
and V
2=V
x,
and so we can write:
Which says that we can determine R
x
in comparison to R
0 provided
that we know
the ratio V
2/V
1.
We can easily show that V
2/V
1=R
2/R
1 and so write the
textbook solution:
R
x = R
0
R
2
/ R
1
but the important point is that we do not need to know the supply
voltage V, and we do not need to know the absolute values of R
1 and R
2,
only their
ratio. Indeed, we do not even need to use resistors R
1
and R
2, because what we
really need is
two voltage references V
1 and
V
2,
of known ratio; which we might, for example, obtain instead by
using two electronically controlled voltagesources in series.
From the above, we
can deduce that
a bridge is a device that measures the ratio of two voltages,
one being a voltage sample taken from across the device under
test, the other being a voltage derived by sampling the current
passing through the device under test. Put more formally:
a
bridge is a device that measures the ratio of a voltage analog
and a current analog, an 'analog' being a quantity that is
analogous to, i.e., proportional to, the quantity in which we
are interested (the British spelling is "analogue";
but the American spelling is nowadays preferable in a technical
context, and helps to avoid creating a world shortage of the letters
u and e). By comparing two quantities that both vary in proportion
to the powersupply voltage, we can make measurements that are
independent
of the powersupply voltage.
Refs:
[
1a]
"Wheatstone's
Bridge" (J A Fleming) The Encyclopaedia Britannica, 13th
Edition 1926. Volume 27.
[
1b]
"
Pioneers of
Electrical Communication  Charles Wheatstone IV". Rollo
Appleyard, Electrical Communication, Vol. 6, No. 1. July 1927.
p212.
[
1c]
The genesis of the
Wheatstone bridge. Stig Ekelöf. Engineering sci.
&
education J. 10 (1), Feb 2001. p3740.
In the paper in Phil. Trans. Roy. Soc. in which Wheatstone described
the DC bridge that now bears his name, he attributes the idea
to S.H. Christie. French and German translations published the
following year and possibly prepared from a preprint of the paper
do not carry this attribution and this might explain why the bridge
does not bear Christie's name. This paper discusses the work of
both Christie and Wheatstone and why the term 'Wheatstone bridge'
and not 'Christie bridge' is used
[
2]
Advanced
Level Physics,
M Nelkon and P Parker, 3rd edition (SI) 1974, Heinemann, London.
ISBN 0 435 68636 4.
Ch 33: Wheatstone Bridge p829.
2. Arms:
Because of their role in determining the ratio R
x/R
0, the voltage splitting resistors R
1
and R
2, are known as the
ratio
arms
of the bridge. Later on, when we generalise the bridge to AC,
we will be able to use devices other than resistors in the voltage
splitting network, but they will still be known as the ratio arms.
The term "arm" hails from the 19th Century, and seems
to have arisen in an ad hoc way for want of terminology to use
while explaining bridges (arms are appendages that splayout from
a node). The term has since acquired a life of its own however;
and nowadays (according to LangfordSmith [
3]), an
arm
is defined as "a distinct set of elements, electrically isolated
from all other conductors except at two points". Hence an
arm is a twoterminal network, and the idea that it is one of
a seriesconnected pair is perhaps less essential. On that basis,
a bridge has six arms.
Ref:
[
3]
Radio
Designer's
Handbook, Ed. Fritz LangfordSmith. 4th edition.
4th impression
(with addenda), Iliffe Publ. 1957 [A later reprint exists (1967)
ISBN 0 7506 36351]
Arm (Definition), section 4.7.
[LangfordSmith's definition is poor. An arm is one of a series
connected pair of two terminal networks in the basic bridge, but
multiterminal networks are also used  eg. transformers]
3. Reciprocity:
In the diagram below, the positions of the meter and the battery
in the bridge discussed earlier have been interchanged.
The swap has made rather a
mess of our original voltage
and current
definitions, and so the circuit is redrawn on the right to make
the analysis more obvious. Using the same arguments as before,
we may observe that, at balance, R
x/R
2=R
0/R
1,
i.e.:
R
x = R
0
R
2
/ R
1
Which is exactly the same result as was obtained previously. This
means that the battery and the meter can be swapped without affecting
the balance of the bridge; or to put it formally: the bridge is
a
linear reciprocal network, its
measuring function
being unaffected by transposition of the generator and the detector.
The term 'linear' refers to the fact that the elements within
it obey Ohm's law, i.e., the graph of voltage against current
is a straight line. If the devices used to make a bridge are nonlinear
(e.g., semiconductor diodes) then the bridge is not a reciprocal
network.
4. Generalising the Bridge:
We may just as well use Christie's bridge by replacing the battery
with an AC generator and the galvanometer with a detector sensitive
to alternating voltages. Analysis of the bridge however then entails
treating all of the voltages and currents involved as phasors;
but (as always) we can satisfy this requirement by writing impedances
as complex numbers and deriving expressions for the voltages and
currents from them. Here we will use the notation and various
simplifying techniques developed in chapter
1. In
particular,
quantities that must be treated as vectors will be written in
bold;
and we are at liberty to nominate one
vector in any
complete set to be a reference vector, and by choosing its direction
to be 0°, may treat it and any other vectors in phase with
it as scalars (i.e., real numbers) [
AC Theory, 24.5].
The AC version of the
bridge, with attendant vectors is shown on the right. In order to
analyse this network, we first observe that V1+V2 must be equal to V0+Vx, and that the voltage across the
detector D (Vdet)
is equal to both V1V0 and VxV2, i.e.,
V0 +
Vx =
V1 +
V2
Vdet
= V1  V0
Vdet
= Vx  V2 

Let us assume, for the time
being, that the detector is
a high
impedance device and that any current that flows through it is
insignificant in comparison to Ix
(In fact, provided that the objective is to balance the bridge
rather than read the error voltage, such an assumption will never
cause any measurement errors because, at balance, the current
flowing through the detector goes to zero). We may then observe
that the two impedances Zx=Rx+jXx and Z0=R0+jX0
carry the same current, Ix,
and
that this establishes the phase relationship between V0, Vx, V0+Vx, and V1+V2. Also, we
may simplify the problem by choosing Ix
as the reference vector and setting its phase to be 0°,
allowing
it to be treated as a scalar Ix
= Ix.
Hence:
V0 =
Ix Z0 = Ix
(R0
+ jX0 )
Vx =
Ix Zx = Ix
(Rx
+ jXx )
V0 +
Vx
= Ix [ R0
+ Rx + j(
X0 + Xx
) ] = V1
+ V2
The only matter we have yet to establish is the relationship between V1
and V2,
but to simplify the analysis, we will start by making the obvious
choice of a voltage splitting network that produces V1 in phase with V2.
Assuming that we also know the relative magnitudes of V1 and V2, we can
then draw voltage phasor diagrams for the system, as below:
The main phasor diagram (left), which represents the
relationship
V0+
Vx=
V1+
V2, is constructed
as follows: A line representing
V0
is constructed by plotting a point, moving right by a distance
I
xR
0
and upwards
by a distance I
xX
0
(or downwards if X
0 is
negative), then
plotting another point. A similar procedure is used to construct
a line representing
Vx.
The end
of
V0 is
placed against the beginning
of
Vx,
and the vector sum
V0+
Vx is obtained
by drawing a line from the beginning of
V0
to the end of
Vx.
Now, since we
have chosen
V1
and
V2 to
be in phase, we know that the associated
voltage phasors must lie in a straight line relative to each other,
and we know that the phasor representing their sum is equal in
magnitude and phase to
V0+
Vx. We therefore divide the line
representing
V0+
Vx
according to the relative magnitudes of
V1
and
V2 to
establish the relationship
between the four principal voltages. The constructions on the
right of the diagram above merely serve to illustrate the point
that the detector voltage
Vdet
is
obtained by drawing a line from the junction of
V0 and
Vx to the
junction of
V1
and
V2.
What is remarkable
about the vector
addition process that takes place, and that should be obvious
by studying the phasor diagram, is that the bridge will not balance
(i.e.,
Vdet
will never reach zero)
unless
V0
and
V1
(and also, by association,
VX
and
V2)
are
equal in both phase
and
magnitude. This means that, despite the fact that there are two
variable elements in the currentsampling arm of the bridge (R
0 and X
0),
there is still
only one way in which the bridge can be balanced once the relationship
between
V1
and
V2
has been established. The balance condition for the bridge is:
Which is the same as for Christie's bridge, but with impedances
substituted for the original resistances and all of the variables
being converted into phasors. If
V2
is in phase with
V1,
then the ratio
V2/
V1
is simply a real number 
V2/
V1 that scales
Z0
to make it equal to
Zx
[
AC Theory,
24.8]. If for some reason, we decide that
V2
should not be in phase with
V1,
then we can analyse the chosen voltage splitting network to derive
a complexnumber expression for
V2/
V1, which can be substituted into the
balance
equation given above to maintain its validity.
What all of this
means, of course,
is that to balance the bridge, we must adjust R
0
and X
0 independently; and the
seriesequivalent
impedance for
Zx
is given by:
Zx = ( R0
+ j X0 ) V2 / V1 
If we arrange for
V2
to
be in phase with
V1
then:
Zx = ( R0
+ j X0 ) V2 / V1 
and if we arrange for
V2
to be equal to
V1
(in both magnitude
and phase) then:
This is obviously the basis for an Impedance Measuring
Bridge. There are however, a few practical subtleties in the matter
of designing impedance bridges; and before moving on to them,
we will first discuss voltagesplitting networks, generators,
and detectors.
5. Voltage Splitting Networks:
In the case of Christie's original bridge, the voltagesplitting
network used (i.e., the pair of ratio arms) was simply a resistive
potentialdivider or a potentiometer. In the process of generalising
the bridge to work with alternating voltages and currents, we
simply replaced the unknown and the reference resistances with
impedances. We now take this process to its logical conclusion
by also replacing the voltagesplitter resistors with impedances.
The relationship between the two voltages obtained may be deduced
by constructing phasor diagrams according to the scheme outlined
below, where the current
I is the reference vector,
and
I=
I:
Fig. 5.1
The magnitude of an impedance is obtained by using
Pythagoras'
theorem, i.e.:

Z = √(R²+X²);
and by Ohm's
law, the magnitude of the voltage across an impedance is given
by:

V = 
I
Z =
I
Z.
The relative
magnitudes of
V2
and
V1
are therefore given by the expression:

V2 / 
V1
= 
Z2 / 
Z1
The phase difference between
V2
and
V1 is
simply φ
2φ
1. where Tan(φ
2)=X
2/R
2 and
Tan(φ
1)=X
1/R
1.
The problem with this
type of network
is that reactance is frequency dependent, and so if we write down
the general expression for φ
2φ
1 we find that the phase difference
between
V2
and
V1
will vary with frequency. This is acceptable if we are trying
to design a bridge for operation on a single frequency, but such
is usually
not the case in the context of RF
measurement.
There is one important exception to this phase variability however,
which occurs when we make φ
2=φ
1 with both impedances either
capacitive or
inductive (or purely resistive); i.e., we specify that the two
voltages must be in phase at all frequencies, which means that
the two impedances must follow the same frequency law. In this
case, Tan(φ
2)=Tan(φ
1)
and so:
In this expression, if we fill in the details of the reactances,
i.e., X=2πfL if inductors are used, or X=1/(2πfC) if
capacitors
are used, we find that the frequency dependent terms cancel, and
that the relationship between
V2
and
V1
becomes frequency independent.
This frequency independence will however only hold to the extent
that the impedance versus frequency laws for the two impedances
are identical, i.e., we are best off using nearideal devices
that can be modelled reasonably accurately as a pure resistance
in series with a pure reactance. What the relationship says however,
is not that the two impedances must be the same, but that the
phase relationship will hold as long as the
ratios X
2/R
2
and X
1/R
1
are the same. Thus we can, if we wish, make
an unequal splitter that maintains the required voltage ratio
over a wide range of frequencies. We might, for example, decide
that we want
V2
to be four times
as large as
V1,
in which case we
simply arrange things so that X
2
= 4X
1 and R
2
= 4R
1.
Recall also that Q
comp =
X/R,
and so the
phase relationship will hold over the range for which the Qs of
the two arms of the voltage splitter remain the same.
Perhaps what is less
obvious, but
most useful of all, is that the phase and magnitude relationships
still hold if the resistive components of the two impedances are
allowed to become arbitrarily small. If we put R
2
= 0
and R
1 = 0 into the equation
above, the result
amounts to ∞ = ∞, which might appear problematic
until
we realise that if the relationship between
V2
and
V1
holds good as X
2/R
2 and X
1/R
1
become arbitrarily close to infinity, then it must hold good upon
reaching infinity. Furthermore, as the resistance terms disappear,
so does the requirement that the resistance must remain in strict
proportion to the reactance. In other words, as the resistance
terms disappear,
V2
and
V1
are forced more and more accurately into phase
at all frequencies. This means, in principle at least, that we
can construct potential divider networks using pairs of capacitors,
or pairs of high Q inductors, which can do as good a job as a
pair of resistors. There is one very good reason for wanting to
do so; which is that reactive potential dividers do not consume
any power, and so will not get hot if we are, for example, trying
to divide or sample the voltage output of a large radio transmitter.
In view of the preceding argument, we can now specify three simple
'frequencyindependent' voltage splitting networks that can produce
two voltages in series, in phase, and in any ratio we may care
to choose. We will now consider the practical merits of these
three networks in turn:
Fig. 5.2. Basic voltagedivider networks.
If we opt for the resistive potential divider, it may
be built
using metalfilm or foil resistors. The resistive network is therefore
a possible choice for an ultrawideband voltage splitter that
will work from DC to VHF, and can maintain an accuracy of 1% or
better without the need for initial adjustment or frequency
compensation,
provided that the resistor values are chosen sensibly and the
the resistors themselves have low reactance. From the discussion
in section
27, we know that film resistors have a
turnover
frequency above which they become capacitive, and that for a typical
wireended resistor with a selfcapacitance of around 0.5pF, the
turnover frequency will occur in the 030MHz range if the resistance
value is greater than about 1 kΩ. There is also an appalling
tendency among manufacturers of cylindrical resistors to cut a
helix into the film to increase the length of the conduction path.
We can therefore only use higher value resistors if both resistors
are to be identical (in which case the
impedances
of the
two resistors will always be identical and
V1
and
V2
will remain in phase), or
if we adopt chip (surfacemount) resistors that have very small
parasitic reactances. In general therefore, low value resistors,
typically of around 50 to 100Ω, are used; which means that
the divider network will load the generator quite heavily and
may produce considerable heat. If this is not acceptable, i.e.,
if high resistance values must be chosen in order to minimise
heating, then the voltage balance will also become susceptible
to stray capacitance effects, which reduce accuracy at high
frequencies,
and detector loading effects, which reduce the sensitivity of
the bridge. A compromise is often necessary, with resistor values
chosen to be higher than required for optimum swamping of stray
capacitances, and compensation for the effects of stay capacitance
obtained by placing one or more trimmer capacitors in parallel
with the resistors.
Capacitors are
inherently highQ
devices when correctly chosen for the job in hand, and so capacitive
potential dividers are capable of good phase accuracy. Component
tolerances are generally broader than for resistors however, and
any stray capacitances will be absorbed into the network. Consequently
it may be necessary to place a trimmer capacitor across one of
the capacitors so that the voltage ratio can be adjusted to the
required value. Capacitors consume no power (neglecting losses)
but the reactance of the network varies with frequency. At very
low frequencies, the reactance becomes extremely high, leading
to low output current capability (from the junction between the
two capacitors) and consequent insensitivity of the bridge. As
the frequency is increased, the reactance falls, and a point will
be reached when the network presents an unacceptably reactive
load across the generator. Care must therefore be taken in the
choice of capacitor values, but a working range of 4 octaves or
more is possible in RF applications. We may also, of course, place
resistors in series with the capacitors (in appropriate proportion
to the reactance, as mentioned previously) in order to limit the
minimum impedance presented to the generator at high frequencies;
or we may place suitably proportioned resistors in parallel with
the capacitors in order to assist the output at lower frequencies.
In the latter case, the network can be designed using the simple
observation that if a reactive network designed to give a particular
voltage output is placed in parallel with a resistive network
designed to give the same output voltage; then the offload voltage
will be unchanged, but the output impedance will be lower (i.e.,
the network will be less susceptible to loading effects). If resistors
are added to the network, of course, their parasitic reactances
must be taken into account. The capacitors also must either have
very small or proportionate parasitic inductances. A small compensating
inductance is sometimes placed in series with one of the capacitors
if the arms of the voltage divider are not physically identical.
The use of capacitive
ratio arms
in RF impedance monitoring applications was adopted by the Collins
Radio Company in the 1950s, and the resulting configuration is
referred to in the manuals of that period as a "modified
Schering bridge". The original Schering bridge that gave
rise to the idea is a highvoltage testset for measuring the
the dielectric losses of capacitors [
4]. Other
authors
[
5], [
6], refer to the capacitive
ratioarm bridge
as the "Micromatch", and the "De Sauty  Wein"
Bridge. In fact, the configuration resembles the De Sauty bridge,
but to name it so in this context would be to miss the point;
which is that the need to replace the arms of Christie's bridge
with impedances is obvious within a particular field of application,
and just about every possible bridge configuration that can be
obtained by so doing is named after someone [
4], [
7].
The author's preference is to refer to the device generically
as a "CRAB" (capacitor ratioarm bridge).
"Modified Schering bridge" (capacitor
ratioarm
bridge) used as a mismatch indicator in the 1950s vintage Collins
180L2 and 3 automatic antenna tuners.
Refs:
[
4]
Electrical
Measurements
and Measuring Instruments, E. W. Golding. 3rd edition,
Pitman,
London, 1949.
Schering bridge, p154158. De Sauty bridge, p214216.
[
5]
"Measuring
RF
Power", Joe Carr [K4IPV], Electronics World, Nov. 1999
p942948. Dec 1999 p10001005.
Part 1: Definitions and dB notation, thermistors, bolometers,
thermocouples, diode detectors. Inline bridges: Micromatch [Christie
with capacitive ratio arms], Monomatch (sic) [two types: Coupled
transmission lines. Current transformer with capacitive voltage
sampling, current summing configuration]. Part 2: Bird 'Thruline'
wattmeter. Calorimeters. Micropower measurement techniques. Mismatch
loss and mismatch uncertainty.
[
6]
The ARRL Antenna Book, 19th
edition, ARRL publ,
2000. ISBN: 0872598047.
Bridge types, p27.4.
[
7]
Modern
Impedance Measurement
Techniques, Alan Bate, Electronics World, Dec. 2002, p1218.
Jan 2003, p1825. Feb 2003, p4956. Mar 2003, p5259.
Review of professional impedance measurement techniques: Basic
bridges. Threeterminal measurements. Bulk metal film reference
resistors. Guard amplifiers. Phase sensitive detectors.
[
xx]
Radio Engineers Handbookk,
F E Terman, 1943, sect. 13, p902  911: Common bridge types.
5a. Inductive voltage splitters:
Although the capacitor ratioarm bridge is attractive for monitoring
the output of radio transmitters, progress in the design of bridges
for accurate impedance measurement depended on a move away from
the idea of discrete or noninteracting arms. The first step in
this direction is to consider what happens when the ratio arms
are replaced by inductors.
Of the basic passive
electronic
components, inductors are the least wellbehaved. They have substantial
RF resistance, which varies with frequency, and they have substantial
selfcapacitance, which may easily give rise to selfresonance
in the frequencyrange of interest. Aircored inductors are also
sensitive to environmental factors, they are difficult to make
accurately, and the introduction of adjustable magnetic cores
(slugs) may give rise to further frequency dependent variations
of reactance and resistance. Inductors might therefore seem to
be the least prepossessing of candidates for construction of voltage
dividers; that is, until we allow mutual inductance between the
two coils and turn the assembly into an
autotransformer.
If the sense of the
windings of
the two coils is the same, mutual inductance increases the inductance
of the series combination and initiates transformer action. This
allows us (in principle) to have the best of both worlds: a large
inductance across the generator to minimise standing current,
and a low impedance output from the tapping point to maximise
detector sensitivity. If the magnetic coupling between the windings
is tight moreover, then the output voltage ratio is precisely
defined by the turns ratio, i.e., (referring to the leftmost
diagram below): 
V2/
V1=N
2/N
1,
and the two voltages are in phase. This configuration was invented
in 1926 by Alan Blumlein, the coupling being achieved by means
of twistedbifilar winding. Blumlein, having a knack for catchy
titles, called his invention "the closelycoupled inductor
ratioarm bridge" [
8]. Further improvement in the
coupling is nowadays achieved by using a closed magnetic path
between the coils, e.g., by winding them (bifilar) on a
highpermeability
ferrite toroid. Extremely wide bandwidths are possible, the lower
frequency limit being dictated by insufficient inductive reactance
and consequently excessive standing current, and the upper frequency
limit being dictated by selfcapacitance effects and core losses.
Design data for ferritecored toroidal coils is given in Section
6.212.
In the central diagram above, we take the inductive
splitter idea
to its logical conclusion by using a true transformer. A bridge
based on such an arrangement is known as a 'transformer ratioarm
bridge' (TRAB), and this approach was developed in the 1940s by
Gilbert Mayo of the BBC Research Department [
50], [
LE300/A
handbook]. A true transformer gives the additional benefit
of DC isolation from the generator, and permits optimisation of
the loading relationship between the generator and bridge network.
The auto transformer
and the tapped
isolation transformer have the advantage that any imperfections
in behaviour manifest themselves in both outputs, and so tend
to cancel. The third option (above right) therefore appears to
be less promising, because any phase or magnitude errors in the
transformer output
V1
will be transferred
into the relationship between
V2
and
V1.
Such errors can be taken
into account however, provided that the transformer is operating
within a defined passband; and compensation for residual errors
is possible. Later on moreover, we will return to the point that
the purpose of the voltage splitter is not to provide a power
supply, but to establish the ratio between a voltage sample and
a current sample. If the ratio can be established in some other
way (which it can) then only one voltage sample is required.
The resistive,
capacitive, and transformer
voltage splitting networks introduced above should be regarded
as the basic building blocks for the ratio arms of WheatstoneChristie
or Blumlein bridges. Later on however, when we start to deviate
from the Wheatstone topology, we will return to the idea of using
voltage sampling networks that have frequency dependent outputs;
not so that we can make bridges that are unnecessarily complicated
and difficult to understand, but so that we can tailor the frequency
response of the voltage sampling network in order to compensate
for the amplitude and phase errors in the output of the current
sampling network.
Refs:
[
8]
The
Inventor of Stereo:
The Life and Works of Alan Dower Blumlein, Robert Charles
Alexander, Focal Press 1999. ISBN 0 240 51577 3.
See also:
British
pat. no. 323037.
[
50] Mayo
Generators and Detectors:
The determination of the resistive and reactive components of
an impedance requires that a measurement should be made at a single
frequency. This can be accomplished in the obvious way, by using
a narrowbandwidth (i.e., sinewave) generator and a broadband
detector; but it can also be done the other way around, i.e.,
by using a wideband generator and a narrowbandwidth detector.
In the latter case, the generator can be either a noise source,
or a combspectrum source (i.e., a lowfrequency signal rich in
RF harmonics), and the detector a radio receiver. When using a
broadband source, it does not matter that the bridge will only
balance at one of the frequencies contained in the generator output,
because the bridge is a linear network, no mixing occurs, and
the detector will only indicate the bridge condition at the frequency
to which it is tuned. In general however, sinewave generators
of reasonably high output are easiest to use.
The most obvious
source to use in
conjunction with a wideband detector is an RF signal generator,
which should have a low level of harmonics in its output. Before
making an expensive purchase however, or embarking on a timeconsuming
construction project, it should be noted that basic bridge measurements
do not require an accurate knowledge of the generator output level.
Only the frequency needs to be known accurately, and an ordinary
radio transceiver is a perfectly capable signal generator in this
respect. The principal drawbacks in using a radio transmitter
as a signal generator are that the output may be rather large,
and fussy with regard to load impedance, and the frequency coverage
of transceivers intended for amateur use is not usually continuous.
Such problems are generally surmountable however, as we shall
now discuss.
The vast majority of
modern commercial
allband HF amateurradio transceivers use power amplifiers based
on circuits originally developed by Helge Granberg (K7ES, OH2ZE)
of Motorola inc. [
9]. These are broadband pushpull
transformercoupled
amplifiers that operate from 1.6 to 35MHz or more, but give relatively
high levels of oddorder (3rd, 5th, 7th, etc.) harmonics. The
amplifier output must therefore be routed through a lowpass filter
selected to give appropriate harmonic suppression for the frequency
of operation. Complete HF coverage requires seven or eight lowpass
filters, switched by means of relays operated by the system
microcontroller,
and the amateur frequency allocations are such that complete amateur
coverage requires a full HF set of filters. Obtaining general
transmitter coverage is therefore often a matter of removing
restrictions
rather than adding functionality; the restrictions being applied
by means of one or more 'transmitinhibit' signals from the
microcontroller,
which usually disable a driver amplifier. Modifications, firmware
updates, or special keypad sequences that disable the legalrestriction
signals are usually known to the manufacturer's service agents,
and might be released to those who have legitimate reasons for
requiring general transmitter coverage. Alternatively, for those
with sufficient knowledge of radio circuitry, it is possible to
devise appropriate modifications by studying service manuals;
and documents describing modifications can often be found via
the Internet. Caution is advised with regard to information obtained
from the Internet however, and the actual effect of any proposed
modification should be assessed carefully by studying the transceiver
circuit diagram. Transceivers that have a transverter socket can
almost certainly be modified, because the transverter output usually
is
a generalcoverage signal, and the point at
which
the
transmitinhibit signals are applied must be in a part of the
signalchain that lies after the transverter takeoff point. The
lowlevel transverter output (a few hundred millivolts RMS) will
also be sufficient on its own if an additional radio receiver
is used as the detector.
One advantage of
using a radio receiver
as the detector is that it will have an approximately logarithmic
input response, due to the action of tha AGC system. When making
impedance measurements, a logarithmic detector response facilitates
the location of the null because the level indicator is never
offscale [See Hatfield LE300A Manual]. It is necessary to use
a 'fast' AGC setting incidentally.
When testing
transmission bridges,
the author uses an old
Kenwood
TS430S 100W HF transceiver as a highpower signal generator.
This unit can be tuned while transmitting, and can be converted
to give continuous transmitter coverage from 1.6 to 30MHz by the
simple expedient of unplugging connector 10 on the RF circuitboard.
For a measuring
bridge with a simple
passive diode detector, an appropriate supply voltage is usually
in the order of 5 to 20 V RMS. This, as we shall see, is sufficient
to ensure acceptable detector linearity, and is low enough not
to exceed the reversevoltage rating of the ubiquitous 1N5711
Schottky diode (V
r m=70 V). A
100 W transmitter
designed for a 50 Ω load, on the other hand, produces a
nominal
maximum output voltage of 70.7 V RMS ( V = √(PR) =
√(100×50)
) and may not give full output or proper harmonic attenuation
unless its load impedance is in a range that corresponds to an
SWR of better than 1.4:1. This means that the transmitter prefers
a load resistance of between 36 and 70 Ω (i.e., 50/1.4 and
50×1.4 Ω); and since the output impedance of a
transistor
transmitter is usually lower than the design load resistance,
coolest running will be obtained if the load resistance cannot
drop greatly below 50 Ω. When using a transmitter to power
a bridge therefore, an intervening network is required in order
to reduce the maximum available voltage and swamp any reactive
impedance that the bridge may present. Such a network might take
the form of a resistive potential divider, of total resistance
not exceeding 70 Ω, rated to handle the full transmitter
output, and designed to give 10 V RMS with the transmitter operating
at about halfpower.
>A suitable potential divider network is shown above.
This can
be built using bulkmetalfoil (Vishay) or other noninductive
resistors, the appropriate power ratings being ≥70 W for the
47 Ω resistor, and ≥30 W for the 20 Ω
resistor.
A
suitable 47 Ω resistor is the Meggitt BDS10047R (RS Stock
No. 2251193), and a suitable 20 Ω resistor is the Vishay
MP93020R (RS stock No. 3204980). Both resistors must be mounted
on a large heatsink. When using a potential divider of this type
incidentally, take care not to exceed the transmitter's continuous
output rating for more than a few seconds (usually about 50 W,
consult the manual), and keep the potential divider away from
anything that might be affected or damaged by heat. Also note
that if the impedance to be measured is an antenna, a small signal
will be radiated, and it might be more appropriate to use a lowlevel
generator and a radio receiver for measurements.
References:
[
9]
Radio Frequency Transistors,
Norm Dye and Helge
Granberg. Motorola inc. / Butterworth Heinemann, Newton MA. 1993.
ISBN 0750690593.
See also:
Diode
detectors for RF measurement. DWK
© D W Knight 2007.
David Knight asserts the right to be
recognised
as the author of this work.