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6.1 Part 1 |
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6.1 Radio Frequency Bridges: Part 2.
Generators and detectors
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<<< 6.1 Part 1. 6-6. Generators and detectors. 6-7. Diode detectors. 6-7a. Half-wave rectifier. 6-7b. Shunt-diode rectifier. 6-7c. Voltage doubler. 6-7d. Bridge rectifier. 6-7e. Bi-phase rectifier. |
6-8. Diode forward voltage drop. 6-8a. Thermionic diodes. 6-8b. Back diodes. 6-8c. Diode non-linearity correction. 6-8d. Diode correction function. 6-9. Diode detector input impedance. 6.1 Part 3 >>> . |
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6-6. 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 narrow-bandwidth (i.e., sine-wave) generator and a broadband detector; but it can also be done the other way around, i.e., by using a wide-band generator and a narrow-bandwidth detector. In the latter case, the generator can be either a noise source, or a comb-spectrum source (i.e., a low-frequency 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, sine-wave 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 time-consuming 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 all-band HF amateur-radio transceivers use power amplifiers based on circuits originally developed by Helge Granberg (K7ES, OH2ZE) of Motorola inc. [9]. These are broadband push-pull transformer-coupled amplifiers which operate from 1.6 to 35MHz or more, but give relatively high levels of odd-order (3rd, 5th, 7th, etc.) harmonics. The amplifier output must therefore be routed through a low-pass filter selected to give appropriate harmonic suppression for the frequency of operation. Complete HF coverage requires seven or eight low-pass 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 'transmit-inhibit' signals from the microcontroller, which usually disable a driver amplifier. Modifications (or keypad hacks) which disable the legal-restriction signals are usually known to the manufacturers' service departments, and may 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 which have a transverter socket can almost certainly be modified, because the transverter output usually is a general-coverage signal, and the point at which the transmit-inhibit signals are applied must be in a part of the signal-chain which lies after the transverter take-off point. The low-level 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 off-scale (See Hatfield LE300A Manual ). When testing transmission bridges, the author uses an old Kenwood TS430S 100W HF transceiver as a high-power 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 circuit-board. For a measuring bridge with a simple passive diode detector, an appropriate supply voltage is usually in the order of 5 to 20V RMS. This, as we shall see, is sufficient to ensure acceptable detector linearity, and is low enough not to exceed the reverse-voltage rating of the ubiquitous 1N5711 Schottky diode (Vr m=70V). A 100W transmitter designed for a 50W load, on the other hand, produces a nominal maximum output voltage of 70.7V RMS ( V = Ö(PR) = Ö(100´50) ) and may not give full output or proper harmonic attenuation unless its load impedance is in a range which corresponds to an SWR of better than 1.4:1. This means that the transmitter prefers a load resistance of between 36 and 70W (i.e., 50/1.4 and 50´1.4 W); 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 50W. 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 which the bridge may present. Such a network might take the form of a resistive potential divider, of total resistance not exceeding 70W, rated to handle the full transmitter output, and designed to give 10V RMS with the transmitter operating at about half-power. |
| A suitable potential divider network is shown above. This can be built using bulk-metal-foil (Vishay) or other non-inductive resistors, the appropriate power ratings being ³70W for the 47W resistor, and ³30W for the 20W resistor. A suitable 47W resistor is the Meggitt BDS100-47R (RS Stock No. 225-1193), and a suitable 20W resistor is the Vishay MP930-20R (RS stock No. 320-4980). 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 50W, consult the manual), and keep the potential divider away from anything which 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 may be more appropriate to use a low-level generator and a radio receiver for measurements on frequencies which lie outside the amateur bands. |
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6-7. Diode Detectors: If a large off-balance output voltage (2-20V RMS) is available, the detector can be one of a variety of simple diode rectifier circuits; although, as we will discuss shortly, consideration must be given to the type of diode used. Note that for any of the diode detector circuits shown below, the polarity of the DC output can be reversed by reversing all of the diodes. 6-7a. Half-wave rectifier. The simplest detector of all is the half-wave rectifier circuit shown below: |
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The DC output of this detector, i.e., the measured voltage Vmeas, is approximately Vdet´Ö2 , where Vdet
is the magnitude of the AC voltage appearing at the detector
port; i.e., Vdet=|Vdet|
. The output is equal to the peak value of the input voltage
provided that the detector load resistance RD
is high in comparison to the output impedance of the bridge network,
and provided that Vdet is large in comparison
to the forward voltage drop of the diode D1.
In this notional diagram, RD is shown
as being separate from the meter, and the meter is assumed to
be a perfect voltmeter, i.e., of infinite resistance. In practice,
RD is usually the resistance of a real
voltmeter constructed by placing a resistor in series with a
microammeter. For example, a 100mA
meter padded-up to 10KW by means of
a series resistor makes a 1V FSD (full-scale deflection) voltmeter.
The smoothing capacitor CD should be chosen
so that the time-constant CD´RD is at least 10 times the period (1/f) of
the lowest frequency at which measurements will be made. If the
lowest frequency is to be, say, 1MHz and RD=10KW, then we want CD´RD to be
greater than 10ms, i.e., CD>1nF. If a meter is used as the indicator,
it makes no practical difference if the capacitor is somewhat
larger than the minimum required, and so 0.1mF
(ceramic disk) is a typical choice; but very large capacitors
(10mF and more) will damp the meter
response and may make it difficult to locate sharp nulls. Note
incidentally, that if the signal generator is amplitude modulated
(e.g., with a 1KHz sine wave), and the time-constant CD´RD is chosen
to be shorter than the period of the modulating frequency (e.g.,
about 100ms or 10KW
in parallel with 10nF), then the indicator may be a high-impedance
(e.g. piezo-crystal) earphone, or an audio amplifier and loudspeaker. The reverse voltage rating for the detector diode (VRM) can be determined by noting that CD is charged to a constant voltage approaching VdetÖ2, whereas the most negative instantantaneous voltage appearing at the detector input is -VdetÖ2. Hence the diode must have a VRM of at least 2Ö2 (i.e., 2.818) times the maximum possible RMS input voltage.
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6-7b. Shunt-diode rectifier. A half-wave rectifier can also be constructed using the shunt diode configuration shown below. This is the prototype of the floating (i.e., ungrounded) detector circuits favoured by the Collins Radio Company in the 1950s, including the mismatch indicator used in the 180L antenna tuner and the Bruene reflectometer bridge. |
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This circuit appears, at first glance, to place a diode across
the detector port; but it does no such thing because of the action
of the coupling capacitor CC. When the
bridge output Vdet first goes negative
(relative to the polarity arrow shown on the diagram), D1 conducts and clamps one end of CC
to ground, causing the capacitor to be charged to the negative
peak value of Vdet (i.e., -Vdet´Ö2). The charge in CC
then remains reasonably constant on the time-scale of the AC
signal, and so the near-sinusoidal voltage at the cathode of
D1 averages about +Vdet´Ö2 instead of zero. The filter
comprising the RF choke and CD removes
the AC component to give a measured voltage of Vdet´Ö2 (neglecting the loading
due to RD), which is the same as for the
ordinary half-wave detector. Since D1
only conducts to keep CD topped-up rather
than throughout the entire negative half-cycle of Vdet,
the input impedance of the shunt diode detector is similar to
that of the normal half-wave detector. With regard to the use
of an RF choke however, the same caveats as before apply; but
note that if the meter has greater sensitivity than needed to
give a good indication of Vdet, then the
overall sensitivity of the detector can be reduced by replacing
the RF choke with a resistor, and the troublesome choke is then
eliminated. Since the voltage at the cathode of the diode averages at +VdetÖ2, the instantaneous peak inverse voltage sustained by the diode will be Vdet2Ö2. Hence, as in the case of the simple half-wave rectifier, the VRM for the diode must be at least 2Ö2 times the maximum possible RMS input voltage.
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6-7c. Voltage-doubler rectifier. Given that RF chokes are bulky and potentially problematic, it is often sensible to try to avoid using them even if sensitivity is paramount (i.e., in situations where the choke cannot simply be replaced by a resistor). This can be done in various ways; the first example, shown below, being known as a 'voltage doubler': |
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In this case, the RF choke of the shunt-diode detector is replaced
by a another diode D2. As before, the
coupling capacitor CC can be omitted if
there is a DC open-circuit looking back into the RF source. The
output of the voltage doubler, Vmeas,
is approximately Vdet´2Ö2,
the reason being as follows: When Vdet
first goes negative, D1 conducts and clamps
one end of CC to ground, causing the capacitor
to be charged to -Vdet´Ö2.
The charge in CC then remains substantially
constant on the time-scale of the AC signal, and so the voltage
across CC is placed in series with Vdet, ultimately causing the smoothing capacitor
CD to be charged, via D2,
to approximately twice the peak value of Vdet
(provided that RD is very large in comparison
to the output impedance of the bridge network). Since this detector
conducts on both positive and negative half-cycles of Vdet, it is actually a type of full-wave rectifier. Due to the clamping action of D1, the voltage at the anode of D2 cannot fall substantially below zero. Hence, since the voltage across CD is +Vdet2Ö2, VRM for D2 must be at least 2Ö2 times the maximum possible RMS value of Vdet. In the case of D1, since Cc is charged to -VdetÖ2 and the maximum instantaneous negative excursion of the input voltage is also -VdetÖ2, then VRM for D1 must also be at least 2Ö2 times the maximum possible RMS value of Vdet.
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6-7d. Bridge rectifier. A detector which requires no RF chokes and does not care of there is a DC path through the network is the full-wave bridge, shown below: |
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This circuit however has two disadvantages; one being that it
has two diode forward voltage drops in the path to the meter,
and the other being that either the meter or the port terminals
must be allowed to float with respect to the system ground. Despite the caveats, one advantage of the bridge rectifier is that the maximum inverse voltage for any of the diodes is only Ö2 times the RMS input voltage. The magnitude of the inverse voltage across D2 is is prevented from rising above VdetÖ2 by the clamping action of D1 and vice versa. The same argument applies for D3 and D4.
6-7e. Bi-phase rectifier. A full-wave detector which has only one diode forward voltage-drop in the path to the meter, and is completely free from grounding problems, is the bi-phase rectifier. |
| By conducting on both half-cycles of Vdet, this circuit also halves the average diode current for a given output voltage and so reduces the diode forward voltage drop compared to that of a half-wave circuit. The disadvantage is that it requires a centre-tapped coupling transformer. The output voltage is given by the expression: Vmeas=Vdet´(Ö2)Ns/Np, neglecting transformer losses and diode forward voltage drop. Correct operation requires that the transformer has sufficient primary inductance not to load the bridge significantly at the lowest frequency of operation, and that the transformer is working within its pass-band. For HF radio frequency applications, the transformer can be wound on a small ferrite toroid or two-hole (binocular or 'pig-nose') core. Note incidentally, that if a transformer is used for the voltage splitting network (ratio arms) of the bridge, it is possible to combine this transformer with the bi-phase detector transformer by using the fact that the bridge is a linear reciprocal network; which results in the configuration shown below: |
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This circuit allows the unknown and reference impedances, the
generator, and the meter, all to have one terminal connected
to ground. The transformer will introduce some minor losses,
but it will not introduce non-linearity unless it is operated
close to core saturation, which is highly unlikely given the
trivial power requirement of a 100mA
meter. A particular disadvantage of this configuration however,
is that it involves stuffing the ratio-arm transformer with a
large amount of wire, which makes it difficult to minimise stray
capacitance between the primary and secondary windings. The ratio-arm
transformer must be designed with great care, and in general
it is best not to try to make it perform additional functions. With regard to diode VRM, note that the bi-phase rectifier is simply two half-wave rectifiers feeding the same smoothing capacitor. Hence the inverse voltage rating for a diode must be at least 2Ö2 times the RMS voltage at the transformer output. As mentioned before, the bi-phase rectifier gives an improvement in linearity over the half-wave rectifier by dividing the rectifier current between two diodes; but as will be discussed next, the diode forward voltage drop varies logarithmically with current in such a way that the improvement will not be particularly large, and so the additional complexity may not be warranted. |
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6-8. Diode forward voltage drop [12]-[17]: All of the diode detectors described above have at least one diode forward voltage-drop in the path to the measuring device. The diode forward voltage drop, Vf, varies approximately in proportion to the logarithm of the current, If, passing through the diode, and also depends on the temperature of the diode junction. For many types of diode, this behaviour is described to a good approximation by a modified form of the Ebers-Moll equation[12]:
   Joules/Kelvin)
, q is the charge of an electron (1.6021892´10 
Coulomb), and T is the temperature in Kelvin, i.e., the absolute
temperature (°C+273.16). The factor kT/q is sometimes given
the symbol VT, and has a value of 25.3mV
at 20°C. "m" is a dimensionless correction factor
between 1 and 2. "ln" is the natural logarithm (Loge). Is is the junction
reverse saturation leakage current.For small-signal rectifier voltmeters, diodes should be chosen for low forward voltage drop and low junction capacitance. Most sources of information now maintain that the best diodes in this respect are silicon Schottky-barrier (i.e., silicon-metal junction) diodes, such as the 1N5711 (Agilent 5082-2800) [18]; and so to investigate this matter, the forward voltage drop versus current characteristics of a variety of small signal diodes were measured. The results are shown in the graph below: |
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The 1N4148 is a silicon P-N junction diode. The 1N5711 is a silicon
Schottky diode. The OA47 is an archaic germanium gold-bonded
diode, and the rest are germanium point-contact diodes. Two 1N4148
diodes from different manufacturers were measured merely to illustrate
the point that silicon P-N diodes have the highest forward voltage
drop and are therefore a poor choice for low voltage detectors.
The 1N5711 curve is the average of results from four diodes,
all from the same batch, which had practically identical characteristics.
The OA47 curve is the average for four diodes from two manufacturers,
all having similar characteristics. The OA90, OA91, and 1N60
curves are from single examples, and are therefore not necessarily
representative of the type. All data were recorded at an ambient
temperature of 21°C. The data indicate that the IN4148, the 1N5711, and the OA47, all obey a logarithmic V/I relationship rather well, whereas the germanium point-contact characteristics show considerable curvature due to high internal resistance. With regard to the forward drop however, the germanium diodes are all superior to the IN5711 in the 1-100mA range, and the preference for the latter may merely reflect the fact that many semiconductor manufacturers can no longer fabricate germanium. Silicon Schottky diodes, such as the 1N5711 and 1N6263, being essentially UHF devices, have better high-frequency performance than germanium diodes, but germanium diodes work well at VHF and are therefore perfectly adequate for HF applications. Among the germanium diodes, there is little difference between the gold-bonded and standard varieties in the 1 to 100mA range, but the OA47 is the best choice for currents up to 1mA. We should observe however, that detector diodes only conduct on the peaks of the applied waveform, and so the instantaneous current is much higher than the average current, the difference being about an order of magnitude. Therefore, in selecting diodes for average currents in the region of 1 - 100mA, we should consider the steady-state voltage drop in the region 10mA - 1mA; in which case the germanium gold-bonded diode offers the lowest forward-drop without contest. Note however, that one of the consequences of the Ebers-Moll equation is that low forward voltage-drop is associated with high reverse leakage current. If reverse leakage is an issue, then silicon Schottky diodes are to be preferred. To put this issue in perspective however, the reverse leakage current of an OA47 diode was measured as follows: |
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| The leakage current is approximately linear in the 5-20V range and may be modelled by assuming a resistor of about 2MW in parallel with the diode. Such a defect has little effect on the operation of a detector loaded with a 10-100KW resistor. Some final points in favour of the silicon Schottky diodes however, are that germanium diodes show a wider spread of characteristics, and that the OA47 is obsolescent. Hence the Schottky diodes are definitely preferable in applications requiring diode matching, precise calibration, or availability through normal commercial channels. The 1N5711 in particular also, has a very high reverse breakdown voltage for a device of its class, its Vr max of 70V making it suitable for half-wave detectors of up to 24.7V DC ouput. An OA47 half-wave detector has a maximum DC output of 10.6V if Vr max is not to be exceeded. |
| Detector diode data: Source: refs. [18], [19] |
| Type | Description |
/ V |
/ mA |
/ mA |
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| 1N5711 | Si Schottky (2.0pF) |
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| 1N5712 | Si Schottky (1.2pF) |
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| AA119 | Ge point contact |
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| AAY30 | Ge Au-bonded. High speed |
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| AAY32 | Ge Au-bonded. High speed |
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| AAY33 | Ge Au-bonded. High speed |
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| AAZ15 | Ge Au-bonded. High voltage |
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| AAZ17 | Ge Au-bonded. Gen.purpose |
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| BAT81 | Si Schottky (1.6pF) |
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0.41 1.0 |
1 15 |
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| OA47 | Ge Au-bonded. Gen.purpose |
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| OA90 | Ge point contact "diode"?** |
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| OA91 | Ge point contact |
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| OA95 | Ge point contact |
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* max. ** a very non-linear resistor pretending to be a diode - best avoided! |
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6-8a. Thermionic diodes: Given that semiconductor diodes are imperfect, some readers may wonder if thermionic diodes (valves) are capable of better performance. The answer however (avoiding expletives) is an an unequivocal 'no!'. The forward voltage of an indirectly heated valve diode in the low-current (space-charge limited) regime (according to Terman [20]) is given by the expression: Vf = [³Ö( If² / k )] - Vc where k is a constant determined by the geometry of the diode and Vc is called the contact potential, by analogy with the potential developed by a thermocouple. The diode contact potential arises because some of the electrons ejected from the cathode arrive at the anode even when there is no bias, and so the anode becomes negatively charged. This means that the diode must be reverse biased in order to prevent it from conducting, and the amount of bias required varies with the heater temperature and the age of the valve. In precision measurement terms, the contact potential is enormous. A sample of eight double-diode valves of type EB91 (6AL5) showed contact potentials ranging from 0.48 to 0.96V (with a mean of 0.73V) when measured using a voltmeter with 10MW input resistance and a stabilised 6.30V DC heater supply (sensible measurement was impossible using a filament transformer connected to the domestic mains supply). A 100mA moving coil meter with an internal resistance of 980W was connected across a diode having an open-circuit contact potential of 0.74V, and registered a zero-bias current of 70mA, i.e., the diode gave a DC output of 4.8mW due to the thermal current. When the meter was padded to 10KW, to simulate the diode loading in a realistic detector circuit, the zero-bias current was 22mA, i.e., 22% of full-scale deflection. We may safely conclude that thermionic diodes have no merit whatsoever in small-signal measuring applications, even if they do glow attractively in the dark. 6-8b. Back Diodes: One further rectifying device which we should mention in passing is the backward diode or 'back-diode' [12], [16], [21], [22], [23]. This is a special type of tunnel diode (Esaki diode), which has an extremely low forward voltage drop: in the region of 90mV for 10mA forward current. Unfortunately however, there is no get-out-of-jail-free card as far as the Ebers-Moll equation is concerned: the back diode has an extremely low reverse breakdown voltage, and a leakage of around 1mA for a mere 500mV of reverse bias. The back diode can therefore only be used in extremely low-impedance low-voltage circuits, which comprehensively defeats any advantage it might have had for the construction of linear detectors. |
 the RF signal
can be amplified to a level where rectifier non-linearity is
no longer severe (and since the sensitivity can now be varied
by some means other than adjusting the meter series resistor,
a single non-linear scale can be used for all sensitivities).
the DC signal
can be fed to an analog to digital (A to D) converter, and the
diode correction applied mathematically. some kind of precision
rectifier can be used (but RF bandwidth can be a problem here). the DC signal
can be applied to a temperature-compensated non-linear amplifier
designed to offset the non-linearity of the detector and produce
an output which is linear overall. |
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The latter method is used in the 'Tandem Match' directional wattmeter
described in the ARRL Antenna Book and elsewhere (Refs [6],[24],[25]. Various approaches are also
discussed in "The Art of Electronics" by Horowitz and
Hill [12]. The use of a wideband
RF amplifier to increase the signal level is described in reference
[26], and other suitable amplifiers
are described in references [27]
and [28]. A diode compensation
scheme involving comparison of the rectified signal against a
voltage level obtained by rectifying a reference sine-wave is
given in reference [29]. Some
years ago, the author invented a linear detector based on sampling
the totem-pole current of a complimentary push-pull amplifier
(see: Linear RMS sensing
voltmeter), but it will be difficult to make it work at 30MHz. A straightforward and reasonably accurate compensation method involves placing a diode in the feedbgack-loop of an operational amplifier and arranging matters so that the resulting gain non-linearity cancels the diode non-linearity. Temperature compensation is inherent, provided that the compensation diode and the detector diode are well matched and in thermal equilibrium (e.g., glued to the same earthed metal plate using thermally-conductive epoxy resin). Two examples are given below, one using a non-inverting amplifier, and one using an inverting amplifier. |
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In order to derive the output voltage of the circuit above, we
start by observing that if the rectification process were ideal,
we would look back into the detector port of the bridge and see
a DC generator producing a voltage |Vdet'|Ö2 via a series resistance Rport, where Vdet'
is the on-load AC voltage and Rport is
the DC path resistance. Because the rectification process is
imperfect however, the effective generator voltage is reduced
by an amount Vf, which is a function of
the average diode forward current If.
Hence the DC voltage appearing at the cathode of the rectifier
diode is: [ (Ö2)|Vdet'| - Vf ] Rd / (Rd + Rport) There being also a voltage drop due to the potential divider formed by the port resistance and the detector load resistance. This voltage is applied to the non-inverting input of an operational amplifier via an RF filter, the component values of which are not critical provided that the resistance is not so large as to exhibit a significant voltage drop due to the amplifier input bias current, and provided that the capacitor is not so large as make the response too slow (say 100KW and 10nF with a good precision op-amp. - not a 741). The output of the amplifier will do whatever is necessary to bring the (+) and (-) input terminals to the same potential. It is wired as a unity-gain follower except for the IN5711 diode in the feedback loop, and by placing a resistor equal to the detector load resistance from the (-) terminal to ground, it is arranged that the feedback diode carries a forward current equal to the average forward current of the detector diode. Hence an amount Vf is added to the output voltage and overall linearity is restored. In practice, unless a chopper-stabilised amplifier is used, it will be necessary to provide an offset nulling circuit. This can be done via the nulling pins of a single op-amp package, or by lifting the earth end of the resistor connected to the (-) input in the case of a dual or quad package. Note that an additional diode has also been placed across the feedback loop to prevent the output from going negative by more than a few tens of mV when the input is zero. The type number given is that of a low-reverse-leakage 'pico-amp diode' (PAD), the point being that the accuracy of the compensation is compromised by any extraneous currents fed into the (-) input. A low bias-current op-amp. is to be preferred for the same reason. In the inverting version of the compensation circuit (shown below), the virtual DC generator is reversed by the equivalent operation of reversing the detector diode. In this case, the output of the amplifier adjusts itself to keep the (-) terminal at ground potential, and so the detector provides a current output into a virtual earth. |
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The topology of the circuit is such that, when the output is
positive, the feedback diode and the detector diode carry a common
average current. Compensation for detector non-linearity is achieved
when the feedback resistor Rs is equal
to Rport+Rd. Notice
that this circuit automatically compensates for the port output-resistance;
which means that minimisation of the DC path resistance is no
longer important, and the practice of shunting ports with RF
chokes can be eliminated. Offset nulling can be provided via
the (+) input terminal if the amplifier has no nulling pins.
Both of the compensation circuits described above will work accurately once the output voltage has risen above a few tens of millivolts. Below that level there will be errors due to offset drift and amplifier input bias currents. There is also a possible error associated with to the fact that the forward voltage drop due to the static current in the feedback diode may not be exactly identical to the forward drop due to the average current in the detector diode (diodes being non-linear), but the author's attempts to quantify this discrepancy did not produce any statistically significant results (i.e., the effect is small or non-existent). Note that single-rail operational amplifiers can be used if all of the ground connections in the circuits given above are returned to an RF-decoupled 'floating earth' maintained at half the power-supply voltage. Before adopting such a messy approach however, consider the use of a DC to DC converter. Modules are available which will produce a clean ±15V output for 9 to 36V DC in, with 1KV or more of isolation between input and output. These allow dual-rail op-amps to be powered easily using a low-cost unregulated plug-top mains transformer, or by hooking on to an existing 13.8V power supply; and the input-output isolation allows the electronics to be referenced to the RF ground without a parasitic earth-loop to the mains ground. |
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6-8d. Diode correction function: The simple diode detector is extremely useful when making accurate RF voltage measurements, because it has an enormous bandwidth (DC to GHz). When using diode detectors for this purpose, mathematical correction for diode non-linearity can be obtained by fitting the diode forward conduction characteristic to an expression of the form: Vf = V1 ln(If) + V0 + IfRds Where Rds is the diode series resistance, V0+IfRds is the forward voltage when ln(If)=0, and V1 is the gradient of the corresponding graph. We can see how this simple correction function comes about by starting with the Ebers-Moll equation and including a term to allow for the fact that the diode will have some ordinary series resistance (Rds). Hence: Vf = If Rds + m VT ln[( If / Is ) +1 ] where VT=kT/q (the choice of subscript being a reminder that it is directly proportional to the absolute temperature). Vf has to go to zero when If=0. Hence the +1 term inside the logarithm bracket is there to set a boundary condition, which is: ln[(If / Is) +1] ® 0 as If ® 0 Is is usually somewhere around 10 Amps
(i.e., 1nA). Hence, in most practical situations, If/Is>>1, and we can neglect the +1 term
without noticeable effect. This leads to the good approximation:Vf = If Rds + mVT ln( If / Is ) But we don't know Is, and so we perform a substitution to capture this lack of knowledge in a dimensionless parameter (Iref / Is). Thus: Vf = If Rds + mVT ln[ (If / Iref )(Iref / Is) ] Now, making use of the identity ln(pq)=ln(p)+ln(q), we get: Vf = If Rds + mVT ln(Iref / Is) + mVT ln(If / Iref ) which is in the form: Vf = If Rds + V0 + V1 ln(If / Iref ) The choice of Iref is arbitrary, and it is normal to use some convenient engineering multiple of Amps (i.e., usually 1mA or 1mA for signal diodes). Hence, adopting Iref =1mA: Vf = If Rds + V0 + V1 ln(If / [mA] ) i.e., the current inserted into the logarithm bracket has effectively been divided by its units to make it dimensionless, which means that all we do in practice is take the logarithm of the forward current in mA to calculate the rightmost term. Now we can rearrange the equation in the form y=a+bx and carry out a linear regression analysis, i.e.; Vf - If Rds = V0 + V1 ln( If ) where y=(Vf - IfRds) , a=V0 , b=V1 , and x=ln( If ) When calibrating a small-signal detector for currents of <1mA, Rds can usually be assumed to be zero if a Schottky or gold-bonded diode is used. The series resistance of germanium point-contact diodes is fairly large however and cannot be ignored. In order to allow for a finite Rds; the trick in calculation (program or spreadsheet) is to make provision for the term IfRds to be subtracted from the measured value of Vf, but initially to set Rds=0. If the regression-line shows significant curvature, Rds can be adjusted by hand or by iteration to get the smallest standard-deviation of fit. Once the parameters V0, V1 and Rds are determined, the function we started with: Vf = V1 ln(If) + V0 + IfRds will return a value of Vf for a given value of If which is good over several decades of current (provided that the temperature is close to what it was when the fitting data were collected). Note however, that the regression function does not have the correct boundary condition to return a true value for Vf when If ® 0; and so If of less than about 100nA should be trapped as an illegal input. Alternatively we can solve for the Ebers-Moll parameters using: V1 = mVT and V0 = mVT ln(Iref / Is) in which case Vf can be calculated from the Ebers-Moll equation directly and the boundary condition at If=0 will be correct.. In an example given in appendix 2, the regression function for a 1N5711 diode (neglecting Rds) was found to be: Vf = 0.158342 + 0.029060 ln(If /[mA]) Volts Taking VT=25.3mV, this gives m=1.15 and IS=4.3nA. Using the Ebers-Moll equation (with the parameters in full precision as calculated from the fit) produces Vf values which are barely different from those given by the fitting function provided that If>>Is (see spreadsheet 1N5711.ods). Note that the determined Ebers-Moll parameters are not necessarily realistic, because Rds had been neglected in this case, but they are accurate for several more decimal places than are required for correcting experimental detector readings (The SPICE parameters for the Agilent 1N5711 are Is= 2.2nA. Rds=25W). Attempting to include the IfRds correction in the fit resulted in a negative value for Rds, indicating that there are insufficient data to determine the extra parameter in this case. |
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In the first instance, we can consider
the power delivered to RD in the limit
that the peak value of the applied voltage Vdet
is very large in comparison to the diode forward voltage drop
Vf. In this case (assuming that the DC
resistance looking back into the port is small in comparison
to the detector load resistance), the detector output voltage
is: Vmeas = Vdet Ö2 . . . . (9.1) |
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and the power delivered to the load resistor is: Pdet = Vmeas² / RD Now, all of this power must come from the bridge output. Therefore, if we define the detector input resistance as Rdet, we have: Pdet = Vdet² / Rdet = Vmeas² / RD and using equation (9.1) gives: Vdet² / Rdet = (Vdet Ö2)² / RD i.e., 1 / Rdet = 2 / RD i.e.,
The limiting input resistance is a reasonable measure of the input impedance when the detector is driven hard, for best linearity. At lower drive levels, the input resistance will be higher, becoming 'infinite' when Vdet=0 because this is the point where the peak value of Vdet becomes equal to the forward threshold voltage of the diode. The limiting 1:2 impedance transformation rule applies to all non-voltage-multiplying detectors. In the case of a bridge rectifier, the limit is harder to approach because the detector places two diode forward voltage drops in series with the output. In the case of the bi-phase full-wave rectifier (assuming a 1:1:1 transformer ratio) the limit is slightly easier to approach, because the average diode current is shared between two diodes. Note that the input impedance of a detector will be slightly capacitive at high frequencies. This is due to the junction capacitance of the diode. For the 1N5711 for example, this capacitance is about 2pF. Hence placing several diodes in parallel is not a preferred method for improving the linearity of broadband or high-frequency detectors. |
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6-9b. input resistance of a voltage doubler. In the case of a voltage-doubler detector, the limiting output voltage is: Vmeas = Vdet 2Ö2 Hence: Pdet = Vdet² / Rdet = (Vdet 2Ö2)² / RD i.e.,
The voltage doubler also has about double the input capacitance of a half-wave rectifier using a given type of diode. |
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6-9c. Input resistance of a half-wave rectifier (accurate
model): That the input resistance of a non-multiplying detector is about half the load resistance is a useful figure to keep in mind; but a somewhat better knowledge is required when designing accurate instruments. This is particularly the case when the instrument must have minimal effect on the system under test, and the detector must drive a relatively-heavy load (such as a panel-meter). A full analysis requires that we account for all of the energy dissipated as a result of the rectification process, and that we do so even though the currents and voltages involved are non-sinusoidal. The solution lies in the fact that a non-sinusoidal waveform can be resolved into a Fourier series (i.e., a sum of sinusoidal waves plus a constant) and there is no interaction between individual Fourier components within the linear elements of a network (see [A1.1]). This means that a network analysis carried out at one particular frequency is not affected by the other frequencies present; and that the transfer of energy from a process occurring at one frequency to a process occurring at another can only occur within a non-linear element (i.e., at the diode junction). Hence we can treat the input to the detector as a pure resistance at the generator frequency, the value of that resistance being defined by the amount of energy transferred. The voltages and currents used in the generator-frequency part of the analysis however will not correspond to the actual RMS voltages and currents. They will instead be Fourier components of the waveforms; the point being that the rectification process will add a DC component and a shower of harmonics to the actual waveforms, but these will not affect the impedance seen at the generator frequency, save that they are products of the energy transfer process. Although the line of attack is conceptually more challenging than linear circuit analysis, the actual derivation is not particularly difficult. Shown below are two equivalent circuits, on relating to the energy delivered by the generator, and one relating to the fate of the energy transferred. The port to which the detector is connected is regarded as a generator with an open-circuit voltage Voc and an output impedance Zout. Both of these quantities are easily determined by analysis of the driving network. The voltage we need to know to complete the analysis however, is Vdet; and this requires that we know Rdet, which is the apparent resistance, at the generator frequency, seen when looking into the detector network. Note that |Vdet| is not measurable using a conventional broadband voltmeter. If the rectifier is configured to give a positive DC output, the actual waveform at the detector input will be a slightly flat-topped sine wave with a negative DC component. |Vdet| is instead the RMS value of the generator-frequency component when it is considered in isolation. |
| The reason that the actual voltage at the diode anode has a negative DC component is that the port has a finite DC resistance. As mentioned previously, the efficiency of the detector is affected by Rport, becoming zero as Rport goes to infinity. The DC voltage drop across Rport effectively backs-off the positive peak value of the input waveform, thereby setting the point at which Vdet can drive the diode into conduction. |
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Note that Rport
and Zout are independent quantities,
even though they may relate to common physical circuit components;
the point being that what goes on in the driving network at the
generator frequency does not interact with what goes on in that
network at other frequencies. It was also mentioned previously
that Rport can be reduced practically
to zero by placing a choke across the detector input; but since
the impedance of the choke then becomes part of Zout, the effect in a broadband circuit is usually
to replace a quantifiable effect with an unquantifiable one. The energy transferred to the detector can be deduced by considering the DC losses and the detector load resistance, as in the lower of the two equivalent circuits. Were the rectification-process perfect, we would see a voltage (Ö2)|Vdet| at the output terminals; but due to the various losses, the actual measured voltage, Vmeas, is somewhat lower. Note that the diode forward voltage-drop has been given a prime, because the the ordinary diode series resistance Rds has been taken-out to be lumped with the other resistances. Hence Vf' is just that part of the forward drop given by the Ebers-Moll equation. Also, since the phase information in Vdet has been lost in the rectification process, it will be convenient from now on to refer to |Vdet| as Vdet. Hence, by inspection, the power transferred to the detector according to the first equivalent circuit is: Pdet = |Vdet|² / Rdet = Vdet² / Rdet . . . . . . . (9.2) and according to the second equivalent circuit it is: Pdet = (Ö2)Vdet Id where: Id = [ (Ö2)Vdet - Vf' ] / ( Rport + Rds + Rd ) . . . . (9.3) Now, to simplify the working, let us define the total DC series resistance as: Rts = Rport + Rds + Rd Hence the total DC power is: Pdet = (Ö2)Vdet [ (Ö2)Vdet - Vf' ] / Rts Which can be rearranged to give the convenient form: Pdet = 2 Vdet² [ 1 - Vf' / ( Vdet Ö2 ) ] / Rts Equating this with (9.2) gives: Vdet² / Rdet = 2 Vdet² [ 1 - Vf' / ( Vdet Ö2 ) ] / Rts i.e.:
The first thing to notice about this result is that Rdet goes to infinity when Vf' = VdetÖ2. This is the limiting condition when Vdet is very small. Also, Rdet
Rts/2 when Vdet
>> Vf', this being the accurate
version of the rule given in section 6-9a.
We do not quite have a solution for Rdet
however, because Vf' depends on Id. According th the Ebers-Moll equation:Vf' = m VT ln(1+Id/Is) but if we look at the definition of Id given by (9.3), we see that we need to know Vf' in order to determine Vf'. Hence, there is no analytical solution for Rdet, but it can still be determined by using a numerical method. The simplest approach is to guess a value for Vf' (Vf'(seed) say) and use it calculate Id. This value of Id is then used to calculate a new value for Vf'. The seed value is then adjusted until it agrees with the final value to a sufficient number of decimal places. Hence the formula for Rdet is a set of equations which have to be solved iteratively: |
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Id = [ (Ö2)Vdet - Vf' ] / Rts Vf' = m VT ln(1+Id/Is) Rdet = (½) Rts / [ 1 - Vf' / ( Vdet Ö2 ) ] where Rts = Rport + Rds + Rd |
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Also, conveniently, we obtain an accurate value for the detector
output voltage from the same analysis, i.e.:
The iterative method of formula (9.4) was used to calculate the input resistance of a fairly typical small-signal detector as shown in the graph below (spreadsheet: det_Rin.ods). The Ebers-Moll parameters are taken from some measurements made on a 1N5711 Schottky diode. |
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In this case (and it depends very much on the chosen circuit
parameters) the input resistance is 2.6% higher than the limiting
value of Rts/2 when Vdet
is 10V RMS. The important design information however, is that
there is less than 10% variation in Rdet
for Vdet in the range from 2 to 10V. Below
2V however, the input resistance rises dramatically and there
will be a distinct change in the AC circuit conditions unless
the driving network has a very low output impedance. The analysis given above has some limitations. Firstly, it is assumed that the smoothing capacitor Cd is large, so that the losses due to DC-side ripple are small. Secondly, the harmonic energy is neglected, but this will be small provided that the clipping-action of the diode is not severe, i.e., provided that Rport is significant in comparison to Rd. Finally, the detector input capacitance does not appear in the analysis; but if this needs to be taken into account, it is best lumped into the AC-side of the network where it becomes part of Zout. |
© D W Knight 2005-2008.
David Knight asserts the right to be recognised as the author of this work.
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6.1 Part 1 |
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