11.9.1.1 Weston standard cell

The highest quality saturated mercury/cadmium-mercury cell has an e.m.f. of about 1.018 620 V at 20°C. The net e.m.f./temperature coefficient is about −40 μV/°C, arising from the two different coefficients of the limbs, each of the order of 350 μV/°C. It is, therefore, important to avoid a temperature differential across the cell by mounting it in oil or air within a constant temperature enclosure (e.g. for 20°C ± 10 m°C, the uncertainty can be only ± 0.4 μV).

Standard cells are stable, the e.m.f. falling by, perhaps, 1 μV per year. For accurate work, regular confirmation of the e.m.f. should be made at an accredited calibration laboratory.

The internal resistance is 600–800Ω. The current drawn from a cell should ideally be zero: in practice it should be limited to a few nanoamperes for a few seconds.

Should a cell be compared with an electronic solid state voltage reference (below), the cell must be presented and removed while the electronic source is switched on.

11.9.1.2 Electronic solid state e.m.f. reference

These devices use the constant voltage property of Zener diodes to deliver highly stable d.c. voltages, usually at 1 V and 10 V levels for direct voltage meter calibrations, and 1.018 61 V to simulate a Weston cell for d.c. potentiometric standardisation. Up to four diodes (each stabilising at about 6.3 V) are used, having been carefully selected for stability, low noise and low temperature/voltage coefficient properties. After further ageing, these temperature-stabilised monolithic devices may be used either separately with a carefully designed operational amplifier, or connected in cascade in specialised networks to achieve the required output p.d. by potential division using highly stable resistors.

It would appear that these devices are excellent transportable standards of voltage (which should be reliable to within 2 μV/year) and they are much more convenient than Weston cells in this respect. Except for the most extreme requirements of accuracy, they could be used as laboratory standards, provided that at least three separate units are available for intercomparison. With more experience and/or minor refinement to these devices, they could shortly replace the Weston cell completely, since at present the Weston cell can be used as a transportable standard to less than 0.5 μV, but only if very great care is exercised.

Typical electronic devices can deliver, say, 5 mA, 10 V from 2 m Ω and 1.0186V from 2k Ω.

11.9.1.3 Potentiometer principle (using groups of matched resistors)

In Figure 11.21 AB is a manganin wire of length a little greater than 1 m, through which the current I from a 2V secondary cell may be varied by means of R. The current is adjusted so that the p.d. between points F and D, 1.0186 m apart, balances the e.m.f. of the Weston standard cell, the balance condition being obtained by use of the switch S and galvanometer G. The volt drop along the wire is now 1 mV per mm length. The switch S may now be set to apply the unknown voltage V_x, and a new balance point H found. Then the length DH in mm represents the unknown voltage in millivolts.

This very simple arrangement is inconvenient in practice. It suffers also from the disadvantage that the precision of the voltage measurement depends upon the precision with which the point of contact of the slider is known. For example, if the length DH is known only to the nearest millimetre, the precision of the voltage measurement would, in general, be less than 1 in 1000. Much greater precision than this is often required, and to obtain it (and to secure a more compact form of apparatus) some elaboration and refinement in the circuit elements is required. Many practical forms of d.c. potentiometer have been devised.

11.9.1.4 Practical potentiometer

The potentiometer in Figure 11.22 is supplied across AB from a 2 V secondary cell through a rheostat R. Resistors R₂, R₃ and R₄ are connected in series between A and B, but the conditions first considered are with R₄ short circuited by the switch at P1. The resistor R₃ is divided into equal sections with 19 tappings brought out to studs, and there is an additional stud connected to a tapping on R₂.

One terminal of the standard cell is connected to a tapping on the parallel resistor R₁, and the other terminal may be connected (when the switch S is in the left-hand position and the key K is depressed) to the point B through galvanometer G. A balance may be obtained with the standard cell by adjusting the rheostat R, and the resistance values are such that the p.d. between successive studs on R₃ is then precisely 0.1 V, and the voltage between A and B a little over 1.8 V. In parallel with the shunting resistor R₂ is the slide wire W. The tapping on R₂ enables a true zero, and small negative readings, to be obtained on W. By suitable choice of the resistance of R₂ and W the voltage range covered by the whole slide wire is a little over 0.01 V.

R₆ is a tapped resistor with 10 equal sections and 11 studs. The total resistance of R₆ is made equal to the resistance of two sections of R₃, and R₆ always spans two sections by means of sliding contacts on the R₃ switch as shown. The total resistance of R₆ and two sections of R₃ in combination is therefore always equal to a single section of R₃ and the potential difference between successive tappings on R₆ is then 0.01 V.

The unknown voltage V_x is applied to terminals connected through the galvanometer switch S to the sliding contact on W and to the tapping on the R₆ switch. If the slide-wire dial has 100 divisions, each division represents 0.0001 V. Thus, for the switches in the positions shown, V_x might be 0.2376 V. The maximum V_x readable, assuming that there are some graduations provided beyond the 0.01 position on the slider dial, is 1.7 + 0.1 +0.0100 = 1.8100 V.

The resistors R₄ and R₅ are introduced into the circuit by opening switch P₁ and closing P₂; this reduces the p.d.s in the potentiometer circuits to one-tenth of those marked. One division on the slider dial would then correspond with 0.000 01V or 10 μV.

Medium- to high-precision potentiometers include a ‘standard cell setter’ so that the actual e.m.f. of the standard cell can be used for standardisation and, subsequently, for rechecking the standardisation during use without altering the measuring dials: this is more convenient, although less accurate than standardising against the dials. The contact T could be the slider of a 10-turn voltage divider with an indicated range, e.g. of 1.018250 to 1.018 750 V in 1-μV steps.

D.c. potentiometers of very high precision have a ratio non-linearity of ±5 parts in 10⁶. A stable current of 50 mA must be provided by an electronic controller, and a high-gain low-noise detector is necessary: this may be a photocell galvanometer amplifier with a display sensitivity of 5000 mm/μV in a 10-Ω circuit.

11.9.1.5 Comparator potentiometer (using m.m.f. balance)

The comparator potentiometer is one of a group of precision bridges employing mutual-coupled inductive ratio arms. The bridges exploit the high m.m.f. linearity and discrimination of a constant current in a variable number of turns.

A simplified network is shown in Figure 11.23. The measuring loop M is magnetically coupled to the balancing loop B by the turns N_m and N_b, respectively, on a magnetic core, which also carries a feedback winding with N_f turns. The feedback network includes an a.c. modulated sensor which actuates an a.c./d.c. electronic control network C_b to change the direct current I_b until a zero m.m.f. condition is achieved in the core.

11.9.1.6 Operation and standardisation

If I_m and N_b are constant, then for an automatically maintained m.m.f. balance N_mI_m = N_bI_b it follows that linear changes in N_m result in corresponding linear changes in I_b. As N_m has in effect a discrimination and linearity of about 1 in 10⁷, these properties are imposed also on I_b. To convert this linear current scale to voltage across R_b, the instrument has to be standardised against a standard cell. The cell, of e.m.f. E_r, is connected (through S1) in opposition to the p.d. across R_m, and balance achieved by use of the adjustable direct-current controller C_m, which is then left to maintain this current level.

The equivalent cell e.m.f. I_mR_m is now connected (through S2) in opposition to I_bR_b, and N_m turns are selected to be numerically equal to E_r. The m.m.f is balanced automatically by the feedback control system and by a small adjustment to N_b so that I_mR_m = I_bR_b = E_r, represented numerically by N_m. With switch S set to S₀ the unknown p.d. V_x is presented through S_x and galvanometer G₁ in opposition to I_bR_b and balance achieved by manual adjustment of N_m. Then N_m is numerically the unknown voltage.

Instruments of this kind are probably the most linear d.c. potentiometers available. They incorporate additional windings that enable the linearity to be checked by the operator. While the actual values of R_m and R_b are not of first importance, it is vital that they should be constant. Resistors are incorporated for subdivision of I_m for lower decades of N_m in order to simulate the 10⁷ turns implied by a discrimination of 1 in 10⁷, but they do not contribute unduly to the overall non-linearity, which is about ± 0.3 × 10⁻⁶ of full scale. The system uncertainty must include that of the standard cell, at least ± 1–2 μV.

11.9.1.7 Pulse width modulation potentiometer¹²

This method subdivides a known stable d.c. voltage in terms of a time-period ratio. If a standard voltage source E_r is repeatedly connected to a low-pass filter through a very-high-speed semiconductor switch for a time t₁, and then disconnected for an additional time t₂, the high-frequency rectangular, chopped waveforms will, after smoothing, give an output E₀ = E_r·t₁/(t₁ + t₂) with t₁ + t₂ = T, a constant period. The time ratio can be precisely set using a variable time-interval counter for t₁ and a fixed-period counter for T, with each counter being driven from a common highly stable crystal-controlled oscillator. An unknown voltage V_x, in opposition to E₀ through a galvanometer, can be measured by variation of E₀ (through the voltage-scaled setting of the t₁ counter) until galvanometer zero balance is achieved. The e.m.f. E_r of the solid state source of steady voltage must be known accurately and the source must be capable of delivering small current surges into the low-pass filter without any significant change in voltage. Conversely, V_x and E_r could be interchanged when V_x > E_r.

One d.c. variable-voltage source uses the accurately determined voltage as input to constant gain d.c. amplifiers (designed for decade steps) to give a wide-range d.c. voltage standard source with ±50 p.p.m. uncertainty (3-month stability) up to 1.2 kV with a 25 → 10 mA (at 1 kV) current capability and 0.5 → 3.0 s settling times.

11.9.1.8 Applications

The d.c. potentiometer may be used to determine temperature by measuring the thermo-e.m.f.s in calibrated thermocouples. In conjunction with standard four-terminal resistors and shunts it is applied to the calibration of voltmeters, ammeters and wattmeters, and for the comparison of resistors. In Figure 11.24 the values V_x, I_x, R_x and P_x are unknowns, and E_p is measured by the potentiometer. Resistors R₁ …, R₇ have known values. At (a) a voltage divider is used to measure V_x, and at (b) a shunt is employed to measure I_x. At (c) R_x is compared with R₄ by means of their respective p.d.s. The network (d) enables the power P_x = V_xI_x to be determined from V_x and I_x. The resistance of four-terminal resistors is known between the potential (inner) terminals, and not the current (outer) terminals, which minimises errors due to non-uniform current densities and contact resistances.

The National Physical Laboratory (NPL) designed ‘Wilkins’ resistor is a high-stability, four-terminal, a.c./d.c. resistor available in various decade and other values (Tinsley Co., London) which has an exceptionally low time constant for accurate a.c./d.c. comparator networks, etc.

11.9.2.1 Larsen potentiometer

The primary winding of a variable mutual inductor is connected in series with a tapped resistor to a source of voltage V. The unknown voltage V_x is normally derived from the same source, because identity of frequency is essential. The supply current I is controlled by resistor R₁ and indicated on an ammeter. The inductor secondary e.m.f. in series with a tapped fraction of the volt drop across R is balanced against the unknown V_x (Figure 11.25) by means of the vibration galvanometer G, the sensitivity of which can be varied by resistor R₂. If M and R are the mutual inductance and resistance values at balance, then

where φ is the phase angle between V_x and I. In practice it may be necessary to reverse either or both of the component voltages to secure balance, and reversing switches are incorporated for this purpose. The mutual inductor should be astatic, to avoid pick-up errors.

11.9.2.2 Gall potentiometer

The Gall potentiometer (Figure 11.26) provides two quadrature voltage components, summed and balanced against the unknown V_x. The supply voltage V is applied to the primaries of isolating transformers T₁ and T₂. The secondary of T₁ supplies a current, approximately in phase with V, to R₁ which consists of a tapped resistor and slide wire in series. The current is adjusted by resistor R₃ and read on an ammeter A, and passes through the primary of a fixed mutual inductor M. Any desired value of in-phase voltage (within the available range) is obtained from tappings on R₁. The primary of transformer T₂ has a series resistor R₅ and a variable capacitor C, and may be so adjusted that the current in R₂ is in quadrature with that in R₁. The exact phase angle, and the calibration of the quadrature circuit, are achieved by balancing the secondary e.m.f. of the mutual inductor M against a fraction of the p.d. across R₂. Thus, variable voltages, phase and quadrature, can be obtained from R₁ and R₂, respectively. These, in series, are balanced against the unknown V_x through the vibration galvanometer G. The reversing switches S₁ and S₂ facilitate balance and provide for a phase angle over a full 360°.

11.9.3.1 Wheatstone bridge

The Wheatstone bridge is an arrangement in very wide use for the determination of one unknown resistance in terms of three known resistances. The network is shown in Figure 11.27, where R₁, R₂, R₃ and R₄ are resistors connected at the nodes a and b through a reversing switch S to a d.c. supply. The galvanometer G, with a shunting resistor to control its sensitivity, and the key K are connected to the nodes c and d as shown. R₁ and R₃ may be set at known fixed values. R₂ is a variable resistor and R₄ is the unknown resistance to be measured. The bridge is balanced by adjusting the value of R₂ until the deflection of the galvanometer, set for maximum sensitivity, is brought to zero. The condition for balance is easily seen to be R₄/R₃ = R₂/R₁ and is independent of the voltage applied to the bridge: whence the unknown is R₄ = (R₃/R₁)R₂. The bridge may be built up as a single unit with, for example, R₁ and R₃ each able to be set at one of the resistance values 1, 10, 100 or 1000 Ω. The bridge ratio R₃/R₁ may therefore have a range of values from 1000/1 to 1/1000. In this case R₂ might conveniently be adjustable, by means of dial switches, in steps of 1 Ω from 1 to 11 110 Ω.

The bridge resistors are wound from manganin wire, since manganin is an alloy with a low temperature coefficient of resistance and a low thermoelectric e.m.f. to copper. Any thermoelectric e.m.f.s in the bridge connections which did not on average cancel themselves out could give a false result. Errors from this cause are eliminated by taking a balance for each position of the changeover switch S and using the mean of two observed values of R₂.

High-precision Wheatstone bridges are capable of measuring resistances between 1 Ω and 100 MΩ with uncertainties which vary between 5 and 100 in 10⁶ of the reading over this range of values. Modern resistors are very stable devices and they should not change in value by more than a few parts in 10⁶ per year; however, it is prudent to check the linearity of resistive bridges regularly, particularly if they are being used to the limit of the original specification. Some bridges have trimming facilities available with the principal resistors, although corrections can always be applied which although tedious, can avoid imposing new resistance drifts on the bridge as a consequence of changing stable resistors.

Various forms of high-quality bridges are used for measuring the changes which occur in resistive transducers. The Smith and Mueller bridges, used for measurements with precision platinum resistance thermometers, can yield 0.001°C discrimination in readings. For strain gauge transducers there are portable bridges that can detect changes of 0.05% or less.

11.9.3.2 Kelvin double bridge

The Kelvin double bridge is an adaptation of the Wheatstone bridge which may be used for the accurate measurement of very low resistances, such as four-terminal shunts or short lengths of cable. In the network (Figure 11.28) R_x is the unknown and R_s is a standard of approximately the same ohmic value. The two are connected in series in a heavy-current circuit (e.g. 50 A for R_s= 10m Ω, giving 0.5 V drop and adequate sensitivity). Suitable values for R₁, R₂, R₃ and R₄ are in each case a few hundred ohms. To use the bridge, R₁ and R₂ are made equal; then R₃ and R₄ are adjusted (keeping R₃ = R₄) until balance is achieved. Then the balance condition is R_x/R_s = R₄/R₂ = R₃/R₁. Provided that it is short and of adequate cross-section, the connection between R_x and R_s does not affect the measurement.

Good-quality commercial bridges claim an uncertainty of about ±0.05% for unknowns between 1 Ω and a few micro-ohms. Near the latter level a small constant resistance becomes a limitation. As R₁, …, R₄ constitute a Wheatstone bridge network, a Kelvin bridge is often extended to measure two-terminal resistances up to 1 MΩ with an uncertainty of ± 0.02%.

11.9.3.3 Digital d.c. low resistance instruments

Digital milliohmmeter/micro-ohmmeter instruments have built-in d.c. supplies; they are auto-ranging and make four-terminal measurements by internal comparator-ratio techniques to give, e.g. 4-digit displays in the case of the Tinsley 5878 micro-ohmmeter with 0.1 μΩ best resolution and uncertainty ± (0.1% → 0.3%) of reading. Also, a IEEE 488 bus attachment is available for use in automated test systems. Thermal e.m.f. balance is incorporated as well as lead compensation.

11.9.3.4 Comparator resistance bridge

The comparator resistance bridge is a variant of the comparator potentiometer (Figure 11.23). In this case the network connections and adjustments are such that, at balance,

where R_b is the known standard four-terminal resistor and N_b has been adjusted to make R_b/N_b an exact decade value. The unknown four-terminal resistance R_m is found in terms of a number of turns N_m and a decade factor.

The two resistors can be compared at different current levels, so that, for example, the rated current can be used with the test resistor, while the standard resistor can be used at a current well below the level at which self-heating effects would change its resistance value. The actual comparison uncertainty with this class of bridge is less than 1 in 10⁶, to which must be added the basic uncertainty in R_b, probably 2 in 10⁶ if it is a class ‘S’ (or ‘Wilkins’) standard four-terminal resistor known to be stable.

(1) Single-purpose or multipurpose a.c. bridge networks, with four or six arms or with inductive ratio arms.

(2) Analogue and digital networks developed for special applications and consisting of frequency-selective or resonant or filter networks; they are associated usually with measurements at radiofrequencies and high audio-frequencies.

(3) Digital multimeter instruments for measuring the modulus of the unknown parameter (but not other qualities).

11.9.4.1 Balance conditions

In the four-arm bridge of Figure 11.29, the arms comprise impedance operators Z₁, Z₂, Z_s and Z_x. The network is supplied at nodes a and b from a signal generator, and a sensitive null detector is connected between nodes c and d. If Z₁ and Z₂ (fixed standards) and Z_s (variable standard) are so adjusted that the p.d. between c and d is zero, then the unknown impedance Z_x depends on whether Z₁ and Z₂ are adjacent as in Figure 11.29(a), or in opposite arms as in Figure 11.29(b); in either case the balance condition is that the product of pairs of opposite arms is equal, giving

where Y_s = 1/Z_s. These are complex expressions, so that the equality involves both magnitude and phase angle; alternatively, both phase (‘real’) and quadrature (‘imaginary’) components. Thus, equation (a) above can be written in terms of magnitudes in either of the following ways:

The bridge arms will include intentional or stray inductance and capacitance, and the corresponding reactances are functions of frequency. Most practical bridges are so chosen that only two or three final adjustments are necessary to obtain the optimum null condition of the detector.

11.9.4.2 Signal source

The bridge supply can be from a screened power-frequency instrument transformer, but more probably from a fixed- or variable-frequency signal generator (see Section 11.7.4). A voltage up to 30 V may be required, but a few volts is normally adequate, especially for radiofrequency bridges. The maximum power of a signal generator is of the order of 1000 mW, so that to avoid overload and distortion it is important that the appropriate voltage be set and a reasonable match be obtained between the generator and the effective input impedance of the bridge network.

11.9.4.3 Detector

A moving-coil vibration galvanometer may be used at discrete frequencies over the range of 10 Hz–1.2 kHz. The galvanometer has a taut suspension mechanically tuned to the operating frequency. The method is sensitive, and effectively filters harmonics, but it is often more convenient to employ the electronic detectors included in most commercial bridges. These include tuned-resonance amplifier networks or broad band high-gain electronic amplifiers; both give a rectified out-of-balance display on a d.c. instrument, with ‘magic eye’ or c.r.o. as possible alternatives. In some portable instruments it was the practice to use head-telephone sets, which are highly sensitive in the audio range of 0.8–1.0 kHz.

11.9.4.4 Bridge-arm components

Precision a.c. resistance boxes can be designed with very low time constants. They are available with switched or plugged groups of ten resistors in decade values between 0.1Ω and 1 MΩ. Careful construction and screening enable some of these devices to be used at frequencies up to 1.2 MHz before the residual reactance becomes significant. An overall uncertainty of ±0.05% is possible, but 0.1–1.0% is more conventional. (See also Section 11.9.1.8.)

Multi-dial switched mica capacitors are available with good stability and low loss tangent. Single- and double-screen capacitors have respectively, three and four terminals, and care is needed to avoid unwanted stray capacitance, the screens being maintained at the proper potentials with respect to the equipment and the environment.

Continuously variable calibrated air-dielectric capacitors with ranges between 20 and 1200 pF are used for small adjustment, and ranges of fixed or variable mutual inductors are available. For high-voltage bridges the standard capacitors are of fixed value, and designed with air or compressed gas as dielectric for 300 kV and above.

11.9.4.5 Low-frequency and audiofrequency bridges

A selection is given of the more important bridges, many of which form the basis of commercial instruments; for example, the inductance bridges of Maxwell and Hay, the modified de Sauty bridges for capacitance, the Schering bridge for capacitance and toss tangent at low and high voltages, and the Wien bridge for frequency and a.c. resistance. These bridges are commonly made to give results with a ±1% uncertainty, but can be designed for ±0.1%.

All bridges should be checked occasionally to show that the reference standard components have not changed and that the range and ratio division has not drifted; also, if the bridge is frequency sensitive, the frequency of the oscillator and the drift rate should be investigated. Naturally, superior standard components must be available which have recent ‘traceability’ certification, in addition to accurately known decade-ratio measurement techniques. Where bridge measurements are implicit in contract specifications, it may be prudent or necessary to justify the claims by referring the instrument to a calibration service standards laboratory.

11.9.4.6 Mutual inductance

Figure 11.30(a) shows the simple Felici–Campbell bridge for the measurement of an unknown mutual inductance M_x in terms of a variable standard M. For balance on the null detector D, then M_x = M, on the assumption that the inductors are perfect, i.e. that the secondary e.m.f. is in phase quadrature with the primary current. Each, however, has a small in-phase component that can be represented by an equivalent resistance σ. The modification in Figure 11.30(b) shows Hartshorn’s arrangement, which enables the impurities to be measured: at balance by adjustment of M and r, the conditions are M_x = M and σ_x = r + σ.

11.9.4.7 Inductance

Inductance may be measured by Wien’s modification of the Maxwell bridge (Figure 11.31(a)). If the unknown inductor has an inductance L_x and an equivalent series resistance R_x, balance gives

The advantage is that inductance is measured in terms of a high-quality and almost loss-free capacitor. The bridge can measure a wide range of inductance values with Q factors less than 10. High Q factors require excessively large values of R₁, and by creating the same effective phase characteristic by means of a low-valued resistor R₁ in series with C₁, the Hay bridge of Figure 11.31(b) is obtained. The balance conditions for it are

A disadvantage is the need to measure the frequency.

A commercial instrument using the Maxwell and Hay bridges has built-in supplies at frequencies of 50 Hz, 1 kHz and 10 kHz, and an inductance range from 0.3 μH to 21 kH with an accuracy within ±1%. The loss resistance is known to about ±5%, and it is possible to introduce a d.c. bias.

11.9.4.8 Capacitance at low voltage

Relatively pure capacitors can be measured by the de Sauty bridge (Figure 11.32(a)), the balance condition for which is C_x = C_s(R₄/R₃). Imperfect capacitors can be compared by the arrangement shown in Figure 11.22(b), in which the imperfection is represented by a series resistance r. To obtain balance, adjustment of all four resistors R is necessary:

For the loss tangent,

Portable commercial capacitance testers, with battery-driven 1 kHz oscillators and rectified d.c. or headphone detectors, use a modified de Sauty bridge network so that loss tangent can be estimated and the capacitance measured to an uncertainty of about ±0.25%.

11.9.4.9 Capacitance at high voltage

Dielectric tests at high voltages, particularly of the loss tangent, can be made with the Schering bridge (Figure 11.33). The bridge is in wide use for precision measurements on solid and liquid dielectrics, and for insulation testing of cables, high-voltage machine windings and capacitor bushings. The capacitance of the high-voltage standard capacitor C_s is calculable, and with an air or gas dielectric can be assumed to have zero loss. A typical standard capacitor for 150kV is shown in Figure 11.34; for higher voltages the clearances necessary for avoiding corona and breakdown are large, but the dimensions can be reduced by a construction in which the dielectric gas is under pressure.

The test capacitor in Figure 11.33 is represented by C_x and a series loss resistance r_x. R₃ is a variable resistor, and the fourth arm comprises a variable low-voltage capacitor C₄ in parallel with a resistor R₄ (which may be fixed). Then, for balance

The loss tangent is a valuable and sensitive indication of the quality of the test insulation. If periodical tests reveal a gradual increase in the loss tangent, then deterioration is occurring, the loss power is increasing and breakdown in service is probable.

To avoid electric field coupling between bridge components–-in particular, between the high-voltage electrodes and the connecting leads–-that would affect accuracy, components R₃, R₄ and C₄ are enclosed in metal screens connected to the earthed point A. Again, to avoid errors due to intercapacitive currents between the centre low-voltage electrode and the guard electrode of C_s, these electrodes should be brought to the same potential by aid of the auxiliary branches C_g and R_s. Balance is achieved with the detector switched to this combination, in addition to the main balance. If the test capacitor C_x is a cable with an earthed sheath, or a capacitor bushing on site and not readily insulated from earth, then the bridge node A must be isolated: careful screening is now even more necessary. Figure 11.35 shows the arrangement for a portable Schering bridge equipment for testing an earthed bushing. It will be seen that an earthed screen isolates the bridge from the transformer primary, and a second screen connected to point A keeps capacitive currents from the high-voltage connections out of the bridge arms.

11.9.4.10 Wagner earth

Capacitance between bridge arms and earth in the Schering bridge causes disturbing currents to flow so that false balance conditions may result. If, as in Figure 11.37, the bridge supply is not earthed but the nodes c and d are at earth potential, then the detector is also at earth potential and no stray capacitance currents can flow in it. Further, all branch capacitances to earth are stabilised. The Wagner earth method secures this condition by the use of the additional impedances Z₅ and Z₆, the junction of which is solidly earthed. Z₅ and Z₆ must be of the same type as either Z₁ and Z₂, or Z₃ and Z₄. If balance is achieved for both positions of the switch, then nodes c and d must have the same potential as the earthed junction, which is zero. Stray capacitance at a and b is innocuous as it merely ‘loads’ the supply.

The Wagner earth is usually applied to commercial Schering bridges, but the technique is applicable to any bridge and can be particularly helpful at higher frequencies.

11.9.4.11 Inductive ratio-arm bridge

The principle is explained by reference to the simplified diagram in Figure 11.38(a), the essential features being the coupled windings of, respectively, N_x and N_s turns. If the voltage per turn is v, then the two windings have the voltages V_x = N_xv and V_s = N_sv, respectively. Let V_x = V_s; then the current I_x through the unknown capacitive admittance Y_x can be made equal to the current I_s by variation of the parallel standards (conductance G_s and capacitance C_s), until the detector shows a null reading. For this condition the standard admittances represent the parallel equivalent network values of Y_x. If Y_x is inductive, the C_s connection at F is transferred to B to avoid the use of standard inductors, which are very inferior to standard capacitors.

The voltage linearity of the input transformer is of fundamental importance to this class of bridge. With modern techniques and magnetic core materials, it is possible to wind toroidal cores to produce an extremely uniform reactive distribution (leakage inductive reactance and turn-to-turn capacitance) with a resultant non-linearity of about 1 in 10⁷ in the magnitude of the mutually induced e.m.f. per turn.

In one well-known bridge (Wayne Kerr) the primary winding of a current transformer is inserted at A and the detector removed to the secondary winding as in Figure 11.38(b). The two parts of the primary winding (n_s and n_x turns) are wound in opposite senses and the detector can indicate the zero m.m.f. condition in the windings.

In general, N_s differs from N_x and n_s from n_x, so that I_xn_x = I_sn_s for balance; further, the primary of the current transformer is at the ground (or earth) potential of the neutral if the trivial resistance drop of the windings is ignored, so that I_x = (N_xv) Y_x and I_s = (N_sv) Y_s. Combining these results gives

The double turns ratio product can be used to permit one accurate standard resistor or capacitor to be switched to any N_s turns of value 1–10 to simulate ten accurate standard components by the precise selection of turns. Moreover, wide-range multiplication of the simulated standard is achieved by decade tappings on N_x and n_x.

An important advantage with this class of bridge is the possibility of connecting the neutral to earth; then small leakage currents from Y_x to earth are almost completely eliminated, since the current transformer is at earth potential and any small leakage currents from the high-voltage side of Y_x merely cause a slight uniform reduction in v but does not alter the turns ratio. Hence, determinations such as the following are possible:

The results of measurements appear in parallel admittance form, and may require elementary computation to render them into series impedance form, with due regard to frequency. With medium to high values of impedance, resistance and capacitance are unaffected, but for inductance measurement (involving a ‘resonance’ balance) a reciprocal ω² correction is needed. For low-impedance networks, resistance and inductance are unchanged but capacitance readings require correction.

11.9.4.12 Characteristics

Universal bridges of the inductive ratio-arm type measure over a wide range of values, at an angular frequency of, e.g., 10 krad/s from a built-in oscillator, or at other frequencies up to 10 MHz using external signal generators and tuned electronic detectors. The measurement uncertainty can be within ±0.1–1.0%, provided that the standard component values are trimmed against superior standards and that the actual frequency is measured when frequency sensitive parameters are measured.

The Wayne Kerr precision bridge operates at 1591.55 Hz (ω = 10 krad/s) and the six-figure display has a minimum uncertainty of 0.01%. The instrument uses an electronic null-seeking process to assist the automatic balancing procedure. With external source the bridge has a frequency range of 0.2–20 kHz with manual balancing.

Admittance bridges are commercially available to operate up to 100 MHz. At this frequency lumped parameter measurements are being displaced by distributed-parameter network characteristics.

11.9.4.13 Current comparator bridge

The a.c. current comparator instrument uses current transformers only in the load network. It is based on the principle, of m.m.f. (i.e. ampere-turn) balance on an ideal magnetic circuit, in which the current ratio is the inverse turns ratio.

The two basic current coils, P and S in Figure 11.39, are wound in opposing senses on a common magnetic core with a high initial permeability. The null m.m.f. condition is sensed by winding M and manual selection of the turns ratio N_p/N_s. The ideal balance condition can be closely approached in practice by shielding the detector from magnetic leakage by a laminated magnetic screen and by a compensation winding W_c. The shield must not form a short-circuited turn; but it does aid magnetic energy transfer between windings P and S. This is advantageous in current-transformer calibration, as it enables an external burden B to be supported under balance conditions. Any change in the capacitive error due to B can be neutralised by W_c connected on one side of the separate centre-tapped transformer W_b. By careful design the capacitance distribution is uniform.

The internal p.d. of the major winding can be neutralised by a parallel compensation winding W_c wound within the magnetic shield, so reducing capacitive currents, as it can be held at earth or reference ground potential.

The commercial range of comparators include d.c. potentiometers, direct voltage and current ratios, d.c. and a.c. four-terminal resistance comparison, voltage- and current-transformer errors, and high-voltage capacitor comparison. All the instruments derived from d.c. and a.c. comparators possess very linear properties, excellent discrimination and good stability. When certified they can be used as comparative reference standards.

11.9.4.14 H. V. capacitance comparator bridge

Standard capacitors used with high-voltage bridges (such as the Schering and comparator types) use compressed gas construction up to a maximum of 1000 pF, although 100 pF is more common. Measurement of such capacitors is based on the principle that a stable alternating voltage to two capacitors produces a current ratio equal to the capacitance ratio. The variable turns ratio of the comparator bridge can be used to balance an unknown capacitor up to 1000 times as large as the standard. By cascading, the range can be extended still further.

11.9.4.15 Substitution

In any active network the equivalent parameters of a component may be measured if variable reference standards can be either substituted for the component or connected in parallel with it–-provided always that the standards can be adjusted so that no final change occurs in the voltage, current, phase or harmonic content of the waveforms in the network. The substitution principle can be applied to any type of bridge, or other class of network; resonant networks often provide the best discrimination between the two conditions. It is important that the stray capacitance, inductance and resistance paths, to earth and between components, should be unchanged by the act of substitution; hence, for the substitution test there should be (ideally) no change in the geometrical layout of leads and components. This can be easily achieved with low-loss changeover switches or coaxial connectors.

For the measurement of radiofrequency components, where shunt capacitance effects are prominent, the substitution principle is particularly valuable. Typical applications are discussed below.

11.9.4.16 Parallel-T network

Figure 11.40(a) shows a general parallel-T network, with an a.c. source as input and a detector across the output terminals. The balance condition (of zero output) in terms of the impedance operators is

Suppose that Z₁ and Z₂ are pure reactances of like sign, e.g. –- jX₁ and −jX₂, and that Z₃ is purely resistive, then

which is equivalent to a negative resistance and capable of balancing out a positive resistance in Z₄ or Z₅. An example is shown in Figure 11.40(b). The source is a modulated signal generator and the detector is, in effect, a radio receiver tuned to the ‘carrier’ frequency. Balance is achieved by variation of C₃ and C₆ with the test terminals open-circuited. If an unknown admittance G_x + jB_x is now connected across the test terminals and the disturbed balance restored by altering C₃ and C₆ to C′₃ and C′₆, respectively, then

Bridge screening is simplified because the common source and detector terminal can be earthed. The use of a variable resistor as a balance arm can often be avoided, a considerable simplification for radiofrequency measurement.

11.9.4.17 Bridged-T network

This can be used at frequencies up to about 50 MHz. Figure 11.41(a) shows the schematic arrangement, and Figure 11.41(b) illustrates a common application. If the unknown impedance Z_x = R + jωL is such that R² is negligible compared with ω²L², then for balance

whence R and L can be obtained if the angular frequency ω is known.

11.10.1.1 Burden and output

Primary currents have preferred values between 1 A and 75 kA, with rated secondary currents of 5 A and 1 A (also 2 A). The rated burden is the ohmic impedance Z_T of the secondary circuit when carrying the rated current I_s at a stated power factor. The rated output is the volt-ampere product (I_sZ_T)I_s. The rated output, the limiting value for which accuracy statements apply, appears in selected preferred values between 1.5 and 30 VA. The normal operating mode of a c.t. is as a low-impedance device; hence, a short-circuiting switch is provided for the secondary winding for use when a low-impedance load (e.g. an ammeter) is not connected to the secondary terminals.

11.10.1.2 Errors

In an ideal c.t. the primary/secondary current ratio is precisely the same as the secondary/primary turns ratio, and the currents produce equal m.m.f.s in exact antiphase. In a practical c.t. the current ratio diverges from the turns ratio, and the phase angle differs by a small defect from opposition. These ratio and phase angle errors arise from that component of the primary current required to magnetise the core and provide for core loss, and from the e.m.f. necessary to circulate the secondary current through its burden. In transformers intended for accurate measurement and for metering, these errors must be small.

11.10.1.3 Classification

The limits of error define the ‘class’ of transformer. BS 3938 defines six classes for measuring and three for protective c.t.

11.10.1.4 Measurement

Errors are normally measured by comparison with a c.t. of higher class. By convention, a phase error is positive when the secondary current phasor leads that of the primary current.

11.10.1.5 Arnold method

In Figure 11.42 C is the c.t. under test and B is a standard of the same nominal ratio and having known, very small errors. The working burden of the test c.t. is Z. The network is such that the difference between the secondary currents I_b and I_c flows in the non-reactive resistor R and is measured by means of the mutual inductor M and slide wire r fed by the auxiliary c.t. F (conveniently of ratio 5/5 A). Phase balance is achieved by adjusting M (positive or negative), and ratio balance by selection of r around the centre-tap of P. From the phasor diagram, the components of the difference current I are approximately I_b–I_c and −jI_c(β_c–β_b) because the phase angles are actually very small. At balance the condition is given by I_b(r–jωM) = RI. Equating the ‘real’ parts gives I_c/I_b = 1 – (r/R); whence in terms of the current ratios k_c = I_p/I_c and k_b = I_p/I_b, where the primary current is common to both c.t.s,

provided that r R. Equating the ‘imaginary’ parts gives

The bridge readings give the errors directly by comparison with those of the reference transformer.

11.10.1.6 Kusters method

This is a comparator method (Figure 11.43) in which C is the c.t. under test with its rated burden Z, and B is an a.c. comparator with the same nominal ratio as C but possessing negligible errors. The errors of C can be deduced directly from the balance settings of the arms of the parallel G – C₁ network.

11.10.2.1 Burden and output

The preferred rated output burdens lie between 10 and 200 VA/ph, and the rated burden is normally the limit for which stated accuracy limits apply.

11.10.2.2 Errors

Five classes are listed in descending order of accuracy, namely AL, A, B, C and D. The voltage ratio error limit varies between 0.25 and 5% and applies for small voltage changes (± 10%) around the rated voltage; and the phase error limits are ± 10 min to ± 60 min from class AL to class C. The phase error of D is not defined.

For dual purpose v.t. (i.e. for both measuring and protective application) additional classes E and F are defined which quote the permitted limits of error for classes A, B and C when used at voltages between 0.05 and 1.9 times rated voltage. The v.t. is then denoted by both relevant class letters. The extended error limits are ± 3–5% and ± 2–5%.

11.10.2.3 Measurement

By convention, a phase error is positive when the secondary voltage phasor V_s leads the primary voltage phasor V_p. The ratio error is (k_rV_s – V_p)/V_p, where k_r is the nominal rated transformation ratio. The rated output is stated in volt-amperes at unity power factor for the specified class accuracy.

11.10.2.4 Dannatt method

This deduces the error in terms of network parameters (Figure 11.44). The v.t. primary is fed from a supply to which is also connected the standard air capacitor C_s in series with a low-valued resistor R_s. The v.t. secondary is loaded with the rated burden Z in parallel with a series-parallel network comprising high-valued resistors R₁ and R₂, a capacitor C₁ and the primary of a mutual inductor M. The secondary voltage of the mutual inductor is balanced against the volt drop across R_s. To ensure that the guard and guarded electrodes of C_s are held at the same potential, a variable resistance R_s is connected so that balance is obtained with either position of the switch S. The balance condition is such that the ratio and phase errors are given very closely by

where L is the self-inductance of the mutual inductor primary.

11.10.2.5 Kusters method

The a.c. comparator bridge can be applied. The capacitance ratio of two gas-filled high-voltage capacitors supplied by a common secondary voltage is measured with the currents passing through the separate balancing windings. If one high-voltage capacitor and its series-connected balancing winding are now fed from the primary supply of the v.t., then the voltage ratio can be found by rebalancing the comparator when the two capacitors are connected, respectively, to the primary and secondary voltages.

11.10.2.6 Capacitor-divider voltage transformer

For high-voltage transformers for 100 kV and above, a more economical and satisfactory voltage division for measurement and protective purposes is given by use of the capacitor-divider system (Figure 11.45). The reduced intermediate voltage appears across the protecting gap G as the input to a tuned transformer. Changes in the secondary burden Z, which would adversely affect the errors, are minimised by adjusting the transformer leakage reactance and/or that of a series inductor L to resonate with the input capacitance (C₁ + C₂) effectively across the primary. There is a consequent sensitivity to frequency.

The classification is the same as for magnetic transformers, except that AL does not apply and there is an additional limitation on frequency. The transient performance is naturally significantly different from that of the normal v.t.

11.11.1.1 Ballistic galvanometer

The moving coil of a galvanometer with a long periodic time gives a first swing proportional to the time integral of the current through it (i.e. the charge) provided that the duration is very short. The charge results from a time integral of voltage (i.e. magnetic linkage) impressed on a known resistance. The moving coil is connected in series with a search coil and a resistor, and is immersed in the magnetic field due to a known current. When this current is rapidly reversed, the total change of linkage is presented to the galvanometer as an impulsive charge, and the first deflection of the instrument is used for calibration against a known (or calculable) linkage change, or for measuring an unknown linkage. The main limitations to accuracy are the observation of the scale and the uncertainty in the current measurement. A typical high sensitivity ballistic galvanometer has a period of 20s, a moving-coil resistance of 850 Ω, and a sensitivity of 8.5 m/μC on a scale distant 1 m from the coil using a lamp and mirror technique.

11.11.1.2 Fluxmeter

The fluxmeter is a permanent-magnet instrument with a moving coil of low inertia and negligible control torque. Its damping is made high by use of a relatively thick aluminium former, so that the period is long. It is immaterial whether the time taken to change the linkage in a search coil connected to the moving coil is long or short, and in consequence the instrument is useful in iron testing, where the time taken for a flux to collapse or reverse may be several seconds. The deflection is read from the initial position of a pointer on a quadrant scale when the pointer reaches its maximum deflection; after this the pointer drifts slowly back to a zero position. A typical full-scale deflection would be given by a change of 10 μWb-t.

Strong air-gap flux densities can be measured by an alternative method in which a small coil is rotated at a high and known speed, the induced e.m.f. being proportional to the local flux density.

11.11.1.3 Hall effect instrument

The Hall effect applies to conductors generally, but its application is normally associated with semiconductor materials. These should be of low resistance so that, even for small signals, the thermal (Johnson) noise effects will be low. Bulk materials, indium arsenide and indium antimonide, have low resistances and good output voltage coefficients, with the InSb voltage larger than that of InAs; however, InAs is usually selected, as its temperature coefficient is one-tenth that of InSb. Thin-film InSb is used for switching applications where the higher output e.m.f. is the prime consideration. The Hall effect response is very fast, being usable up to the megaherz range. Bulk material InAs elements are more effective than thin-film elements, owing to the much lower resistances obtainable.

In commercial instruments the current I_c in the sensing element can be a direct current chopped at audio frequency; the resultant audiofrequency Hall voltage E_H, after linear amplification and demodulation, can be displayed on a taut-band d.c. moving coil indicator against a calibrated scale of flux density. Typical ranges have full-scale deflections between 0.1 mT and 5T for steady fields. Pulsating fields can be measured with d.c. instruments at frequencies up to 500 Hz with a cathode-ray-oscilloscope detector. Instruments for alternating fields only are available for frequencies of about 30 kHz, with ranges similar to those of d.c. instruments.

An instrument and probe can be checked by use of stable reference magnets, which may have uncertainties of 0.5–1.0%. The overall uncertainty of a scale reading is typically ± 3% of the full-scale deflection for the range.

The sensing elements are protected by epoxy glass-fibre or similar enclosures, and are available in a variety of forms for probing transverse, coaxial or tangential fields. The flat form is most common, typically with the dimensions 0.5 mm × 4mm × 25 mm. Incremental measurements, using two matched probes and backing-off networks, enable perturbations as small as 0.1 μT to be observed either in the presence of, say, a given 0.1 T field or as a difference between two separate 0.1 T field systems. Hall effect instruments have many obvious applications where the magnitude and direction of the field distribution is required such as air gaps of machines and instruments, magnetron magnets, mass spectrometer fields, residual interference fields, etc.: in addition, the Hall-effect principle can be used in a variety of transducer applications by making I_c and B proportional to separate physical functions, and measuring the instantaneous or average results of this product. One example is a wide band, 50 kHz wattmeter in which I_c and B are made, respectively, proportional to the scalar values of the load current and voltage.

11.11.2.1 Core loss

In a low-frequency test the loop area of the B/H relation is directly proportional to the core loss per cycle of magnetisation, which provides a simple comparative test for specimen material. A more convenient method employs low power factor wattmeters, but care is needed to exclude instrument and connection losses. Selected samples of sheet steel intended for the cores of inductors and power transformers are prepared for testing in the form of strips (e.g. 30 cm × 3 cm) assembled in bundles and butted or interleaved at the corners to form a hollow square. The sides are embraced by magnetising and search coils of known dimensions. Input power and current, and mean and r.m.s. voltages, are read at various frequencies and voltages to assess the overall power loss within the material and (if required) an approximate indication of the eddy and hysteresis loss components. The Lloyd–Fisher and Epstein squares are commonly used forms, the latter being referred to in BS 601 (Sheet steel).

The magnetic properties of bars, forgings and castings are derived from galvanometer or fluxmeter measurements (BS 2454). A.c. potentiometer and bridge methods are also used, especially for low-loss materials at frequencies in the audio range. With ferrite and powder cores, as with Q-value tests of a coil with and without a slug core, r.f. resonance methods are convenient.

Production and quality control test equipment for core-loss and coil-turns instruments include a ‘coil-turns tester’ (Tinsley 5812D) with a four-digit display of the number of turns in non-uniform and uniform windings, by using an inductive comparative measurement against a standard winding: the same range of ‘magnetic type’ instrumentation includes a ‘shorted-turns tester’ which will detect single and multiple shorted circuited turns in coils of any shape or number of windings; while a ‘core tester’ can check transformer core characteristics of EI stacks, C cores and toroids including hysteresis loop output for a cathode-ray-oscilloscope display.

11.11.3.1 Campbell method

The specimen, shown as a toroid, is uniformly wound with N₂ secondary turns, overlaid with N₁ primary turns (Figure 11.46(a)). The magnetising current I₁ passes through the primary of the mutual inductor M and the resistor r. At balance indicated on detector D, the power factor and power loss are given by

The corresponding magnetising force and flux density are found from

where l is the mean length of the magnetic path in the toroid, a is its cross-sectional area, and V is the mean voltage as measured on the high-impedance average voltmeter V.

11.11.3.2 Modified Owen method

The toroidal specimen (Figure 11.46(b)), has N₁ a.c. magnetising turns, and an additional winding N₂ through which a steady polarising d.c. excitation can be superposed. The d.c. supply is taken from a battery through a high-valued inductor to minimise induced alternating current from N₁. The Wagner earth arrangement R₅C₅C₆ may be added to eliminate earth capacitance errors from the main bridge arms by balancing in both positions of the switch S. The high-impedance voltmeter V measures the r.m.s. voltage V across R₃. The a.c. magnetising force H_a due to the current V/R₃ in N₁, the d.c. magnetising force H_d due to I_d in N₂, the power loss in the specimen (including the I²R loss in the winding N₁ which can be allowed for separately) and the peak flux density B_m are given by

where a is the cross-sectional area of the specimen, and it is assumed that all time-varying quantities have sinusoidal waveform and angular frequency ω.

11.12.1.1 Pure-metal sensors

Pure conductors such as Pt, Ni and W have low resistance/temperature coefficients but these are stable and fairly linear. Pt is generally adopted for precision measurements and, in particular, for the definitive experiment within the range 100–903.5 K of the International Practical Temperature Scale. Platinum and other metals can be deposited on ceramics to produce metal-film resistors suitable (if individually calibrated) for temperature measurement.

11.12.1.2 Platinum resistance thermometer

To a reasonable approximation the resistance R of a platinum wire at temperature θ (in degrees Celsius) in terms of its resistance R₀ at 0°C is

The temperature θ_P for a given value R is

and is known as the platinum temperature. Conversion to true temperature is found from the difference formula

The value of δ depends upon the purity of the metal. It is obtained by measurement of the resistance of the sensor at 0, 100 and 444.67°C, the last being the boiling point of sulphur. The value of δ is typically 1.5.

A practical sensor usually consists of a coil of pure platinum wire wound on a mica or steatite frame, the coil being protected by a tube of steel or refractory material. The resistance measurement is carried out by connecting the coil in a Wheatstone bridge network or to a potentiometer. In the former case the bridge usually has equal ratio-arms and a pair of compensating leads is connected in the fourth arm. These leads run in parallel to the actual leads from the sensor coil and compensate for their resistance changes. If the initial resistance and coefficient k of the sensor are large, the compensating leads may not be required. Figure 11.47 shows the method of connecting three such coils in turn in a Wheatstone bridge network, so as to measure the temperatures at three different locations. In this case the bridge is not balanced; the out-of-balance current through the galvanometer gives the temperature directly. Initial setting is done by adjustment of the battery current until some definite deflection is obtained, when a standard resistance replaces the sensors in the bridge circuit.

11.12.1.3 Thermocouple sensors

Thermocouple sensors are active transducers exploiting the Seebeck effect developed between two dissimilar metals when two junctions are at different temperatures. The International Practical Temperature Scale is defined in terms of a (0.9 Pt + 0.1 Rh)/Pt thermocouple over the range 903.5–1336K. Readings between 100 and 3000K are possible with Au/CoCu at the lower and W/Re at the higher end. Conventional materials for intermediate ranges include

the figures giving the upper limits. The thermo-e.m.f. varies between 10 and 80 μV/K. To make an instrument direct-reading for the temperature at one junction, the second (‘cold’) junction must be kept at a reference temperature. The cold junction can be maintained at 0°C by immersion within chipped, melting ice in a thermos flask, or by using a commercial ice-point apparatus working upon the Peltier effect. When high temperatures are being measured, the terminals of the detector can sometimes be used as the ‘cold’ junction, but compensating leads should be connected between the thermocouple and the detector. The most accurate method for measuring the e.m.f. is with a d.c. potentiometer.

The e.m.f. e for a hot-junction temperature θ (in degrees Celsius) with the cold junction at 0°C is of the form log (e) = A log(θ) + B, where the constants A and B have, for example, the values 1.14 and 1.36 for copper/constantan, with e in microvolts.

The small thermal capacity of thermocouples makes them suitable for the measurement of rapidly changing temperatures and for the temperatures at particular points in a piece of apparatus. One useful application is the measurement of surface temperatures, in which case the thermocouple consists of the two metals in the form of a flat flexible strip with a welded junction at the centre, this strip being applied to the surface under test.

11.12.7.1 Resistance-wire, p–n junction and carbon gauges

A grid of resistance wire is cemented between two insulating films. The grid is usually smaller than 30 mm × 15 mm, and has a resistance in the range 60–2000Ω. When the gauge is cemented to the surface under test, the change ΔR in total resistance R due to a displacement ΔL in a length L is converted into strain ε by means of the gauge factor

If F represents the force and E the elastic modulus (i.e. the stress/strain ratio), then

where a is the area normal to the direction of the applied force. Resistance-wire strain gauges have been in use for many years. Recent developments include metal-foil strain gauges based upon printed circuit and photoetching techniques: these can be made smaller. Thin-film techniques have been developed to apply the gauges directly to very small surface areas.

Semiconductor silicon junction strain gauges are perhaps 30 times more sensitive than the resistive gauge; however, their stress and temperature ranges are more restricted, and they are more difficult to ‘cement’ in position. The inherent non-linearity of the response by sensors can be offset by special bridge techniques using compensation networks.

Gauges consisting of a layer of carbon, which responds to strain in a manner similar to that of a carbon microphone, have a gauge factor typically of 20, considerably higher than for metals but much less than for p—n junctions. The inherent disadvantage is sensitivity to temperature and humidity.

11.12.7.2 Strain-gauge measurement techniques

11.12.8.1 Sensors

For the purpose of detecting surface and submarine ships, magnetostriction transducers have been employed using under-water supersonic vibrations. The compression stresses generated by the transmitter are reflected by the submerged object and are picked up by a detector utilising the inverse effect–-i.e. change of magnetic properties under mechanical stress.

The presence of flaws, air pockets or impurities can similarly be detected in some opaque substances (e.g. rubber) which should normally be homogeneous. The phase displacement between the incident and reflected waves can be interpreted to indicate the position of the obstruction.

Liquid level can be controlled by a sensor probe just above the required level and connected to an oscillator network. As the level of the liquid reaches the probe, the oscillation ceases because of the greatly increased damping. For the measurement of mechanical stress (Figure 11.52) the bridge is balanced when the sensor and compensating elements are equally stressed, the compensating element eliminating thermal errors. If the stress in the sensor element is increased, its permeability is reduced, and the out-of-balance current is indicated on the detector D, which can be calibrated in stress units. If the stress is rapidly varying, D can be replaced by a cathode-ray oscilloscope.

11.12.9.1 Angular velocity sensors

Measurements can be read from the output of a permanent-magnet d.c. tachometer for speeds up to 3000 rev/min. The instrument is direct-reading, but a proportional direct output voltage can be used as an electrical transducer. For low speeds the commutator ripple can be excessive and an a.c. tachometer with full-wave rectification will provide a more uniform output, particularly if the instrument is of the multi-tooth variable-reluctance type. These instruments act as loads on the source and they are unable to assess the fine detail of the angular velocity such as superimposed small amplitude oscillations, or non-uniform accelerations and retardations due to changes in load. Simple optical solutions to the problem involve the use of a stroboscope or photosensor coupled with digital counters, and each method avoids any loading of the machine.

11.12.11.1 Photovoltaic

Photovoltaic sensors are p—n junction devices with the normal barrier layer potential present between the two materials. When illuminated, the higher-energy protons raise electrons from the valence into the conduction band to create electron–hole pairs. The consequent continual charge separation is enough to drive current through a resistive load without any external source.

11.12.11.2 Photoresistive

A photoresistive sensor consists of a single homogeneous semiconductor material such as n-type cadmium sulphide or cadmium selenide. The material is doped to permit of a large electron charge amplification by the selective absorption of holes, and a spectral response that can simulate that of the eye. This type of sensor is well known as a photographic exposure meter. The CdS sensor is not quite linear over wide illumination ranges, and its response time (100 ms), is slow compared with that (10 ms) of the CdSe type.

The sensors can be used in series with a source and a relay, the latter operating when illumination reduces the sensor resistance to about 1 k Ω. The power dissipation by the sensor can be minimised if the slow resistance changes are used to alter the state of a conventional Schmitt trigger circuit (Figure 11.54). The required illumination level is set by R₁; when the illumination is reduced, the cell resistance rises to switch on T₁, which causes T₂ to switch off and T₃ then saturates. The relay operates when the Zener diode conducts at about 12V. The sensor is useful for alarm circuits, street-lighting control and low-rate counting.

11.12.11.3 Photojunction

Normal diodes and transistors are light-shielded. In the photojunction devices controlled light is admitted to enhance the light effect.

11.12.11.4 Photoemissive

Photoemissive sensors are vacuum or gas-filled phototubes. The emission of electrons from the cathode occurs when light falls on it, to be collected by a positive anode. Vacuum phototubes have been superseded for light measurement by photodiodes. In the photomultiplier tube the vacuum emission is enhanced by secondary emission at a succession of anodes to give an electron multiplication of 10⁸ or 10⁹, providing significant output for flashes of very short duration. The photomultiplier is used as a scintillation sensor by viewing the weak light emissions that occur in selected phosphors exposed to α, β or γ radiation. These scintillation ‘counters’ have wide application in spectrophotometry, flying-spot scanning, photon counting and whenever a very weak light signal is to be amplified. An alternative device is the Bendix magnetic multiplier. This consists of a single layer of resistive film with the emissive cathode at one end; by suitable accelerating p.d.s applied along the film, together with shaped magnetic fields, the electrons are multiplied by secondary emission and bounced along the strip to accumulate on an anode to give an overall electron gain of 10⁹. With different emissive materials, ultraviolet rays and X-rays can be amplified for subsequent analysis.

11.12.11.5 Selection

Photovoltaic cells do not require an external supply, but they are generally less sensitive than photoresistive types, which do. Photodiodes can be selected for a range of optimum spectral sensitivities and are fast-operating, particularly so for the silicon planar p–i–n type. Phototransistors provide amplification at the cost of a relatively slow response (minimum 20 μs). Photomultiplier tubes provide high amplification, even for single photons.

Integrated-circuit chips about 4 mm² in area, produced with progressively more complex networks, can include scores of photodiode arrays, with amplifiers, logic counting networks, scanning circuits, etc., to give such outputs as digital pulse rates proportional to illumination, logic for character recognition and punched-card reading, and as replacements for photomultipliers. These devices find a wide range of application in transducer instrumentation for control and communication.