Audio-frequency current comparator power bridge: development and design considerations

The development, design, construction, and partial evaluation of a system for performing active and reactive power measurement from 50 to 20 kHz is described. The technique is an extension of a power bridge based on a current comparator capacitance bridge that was originally restricted to power frequencies. The design features and component characteristics for wideband operation are emphasized. A digitally synthesized, dual-channel signal source provides the required voltage and current signals. >

I. INTRODUCTION CTIVE AND reactive power measurements at fre-A quencies above the normal frequency range of 50-400 Hz are becoming more commonplace in equipment where weight and efficiency are of prime concern. Standards to support audio-frequency wattmeters exist in the form of dual-channel digital sampling instruments [ 11. While sampling techniques are very powerful (particularly when measuring highly distorted waveforms), uncertainties smaller than +O. 1 percent (f 1000 ppm) are difficult to achieve over the audio range. At power frequencies, uncertainties of f 1 5 ppm are achieved using impedance bridge techniques which ultimately rely on thermal voltage converters to relate the ac voltage to a dc voltage standard, and an accurately known ac resistance [2], [3]. The system described in this paper extends this technique to 20 kHz while maintaining measurement uncertainties under 5200 ppm of apparent power.

MEASUREMENT SYSTEM A . Operating Principles
A block diagram of the audio-frequency power bridge is shown in Fig. 1. As in a previous system 121, the wattmeter under test (MUT) is supplied by a dual-channel digital waveform generator followed by power amplifiers AV (voltage) and A, (current). The test voltage is scaled from 120 or 240 V to 10 V with a two-stage transformer. Two such transformers are required to cover the audio-frequency range-one for frequencies between 50 Hz and 1 kHz and the other for frequencies between 1 and 20 kHz. The test voltage is determined by measuring the low-level output of one of these transformers using a thermal ac-dc voltage comparator (TVC). Reference currents I , and Z2 are established with wide band, active binary-inductivevoltage dividers (BIVD's) and impedances R and C. The center-tapped symmetry of the BIVD's provides excellent frequency response [4] and thus only one divider for each impedance ( R and C ) is needed to cover the audio range. The test current Z(O.5-10 A) is compared with the sum of I, and Z, (1 mA) in one of two specially designed current comparators which are required to span the audio-frequency range. The crossover point between the low and high frequency comparators is also about 1 kHz. At balance the active power, P , applied to the wattmeter under test (MUT), may be expressed in terms of where V the applied voltage, R the resistance connected between BIVD, and the k a constant involving the c ent comparator, volt-current comparator (Fig. l), age transformer, and BI r D ratios.

B. Digitally Synthesized Source
The signal source is a digital waveform generator [SI which synthesizes two low-level sinusoidal signals at frequencies between 50 Hz and 20 kHz. In this technique the waveforms are constructed by sequentially applying up to 2048 values stored in read/write memory to a pair of multiplying digital-to-analog converters (MDAC's) which produce voltage waveforms with peak amplitudes between 0-10 V. The amplitudes are independently adjustable by controlling the dc references of each MDAC. The phase relationship of the two signals is adjusted by changing the set of values stored in one of the memories. These signals are applied to high-voltage amplifier AV [6] and U.S. Government work not protected by U.S. copyright transconductance amplifier A, [7], which then supply synthetic power to the MUT.
The voltage and current are programmable between 0-280 V and 0-7 A, respectively, with a precision of 4 ppm of full scale. The phase angle between the voltage and current waveforms may be adjusted with a precision of 1-100 prad, depending on the frequency. The shortterm stability of the power applied to the MUT is typically f 10 ppm. This is further enhanced by a servo-loop (described later), which slaves the test current to the test voltage.

C. Voltage Circuit
Referring to the detailed circuit diagram shown in Fig.  2, a two-stage, voltage transformer TI is used to scale the test voltage I/ to I/, (nominally 10 V). This voltage is measured by comparing it to a 10-V dc reference using a thermal ac-dc voltage comparator similar to the one described in [8]. The magnitude and phase of the test voltage is computed based on this measurement and a knowledge of the transformer in-phase and quadrature errors.
Both the BIVD's and the TVC present substantial loads to the transformer and the technique for minimizing loading errors is shown in Fig. 2. The BIVD's are constructed as two-stage dividers and, thus their magnetizing currents may be supplied from a separate set of windings ( N 4 ) on the main core of TI. This induces the approximate operating voltage across the BIVD ratio winding and effectively increases its input impedance by a factor 1000 or more (depending on the first-stage errors of the transformer and divider).
A similar technique involving an operational amplifier is used to increase the effective input resistance, RT, of the TVC. Amplifier A I , with a gain of two, produces a 20-V signal which is connected to the TVC through resistor RT1. If RTI is approximately equal to RT, A , will supply most of the TVC input current. The ratio winding, N3, of the transformer must supply only the error current required to maintain the precise 10-V level at the TVC. Thus the effective input resistance to the TVC may be increased by a factor of 1000 or more (depending on the gain of A , and the ratio R T / R T l ) .
This "current pump" circuit is very effective at power frequencies where the amplifier can precisely double its input voltage; however, at higher frequencies performance is degraded somewhat by amplifier phase errors.
As mentioned, two voltage transformers are required to span the 50 Hz-20 kHz frequency range. The low-frequency transformer, designed to operate between 50 Hz-1 kHz was constructed using a large magnetizing core with 1200 primary turns ( N I ) . The BIVD drive winding N4 consists of 100 turns tapped for different voltages. The primary ratio winding N2 (also 1200 turns) and the secondary ratio winding N3 (100 turns) are wound around both the magnetizing and ratio cotes (see Fig. 2). The high frequency transformer, designed to operate between 1-20 kHz, is constructed with smaller cores and fewer windings to minimize interwinding capacitance. The maximum in-phase and quadrature errors of these transformers are given in Table I (see Section 111).
The reference currents I, and Z2 are generated by scaling the voltages applied to R and C using 24-bit, two-stage binary inductive voltage dividers. Three 8-bit sections are cascaded to provide 24-bit precision, and the first two sections are coupled using two-stage techniques to minimize loading effects. As in the voltage transformers described above, an extra winding on the magnetizing core is used to drive the following stage. Each section consists of 8 center-tapped windings in a binary sequence (256, 128, 64, . * * , 2 turns) which are interconnected using relays P I .
Because the impedances used to generate I, and Z2 are small compared to the output impedance of the BIVD's, the "current pump" circuits shown in Fig. 2 must be employed. Similar to the circuit used with the TVC, amplifiers A, and A3 provide most of the load current and the BIVD's must supply only the small current required to correct the voltage developed at the terminals of R and C.
Each binary section consists of a twisted pair connected in series to provide the center tap. This technique leads to fairly large interwinding capacitance; however, because of the symmetry of the windings, the center tap is extremely accurate over a wide frequency range and a single BIVD operates over the entire power and audio range. The maximum in-phase and quadrature errors (based on comparisons with decade divider standards) are given in Table I. .

D. Current Circuit
Reference current I, (0-1 mA) is defined by V , d l / R , where d , is the ratio of BIVD, and R is a 4-terminal, 10k!2 metal-film resistor. The maximum in-phase and quadrature errors of this resistor (based on comparisons with calibrated film resistors and standard capacitors) are given in Table I.
Reference current 1, (also 0-1 mA) is defined by: VI d2 j o C , where d2 is the ratio setting of BIVD, and C is one of four three-terminal capacitors needed to cover the frequency range 50 Hz-20 kHz. At the higher frequencies gas capacitors may be used to produce the desired reference current. These capacitors have very low losses and small temperature coefficients. At lower frequencies where larger value capacitors are needed to produce the required current, polystyrene-dielectric capacitors were selected. These capacitors have relatively low losses (dissipation factors of 50-100 ppm compared to 10 or less for gas dielectrics), which are quite stable with temperature and time.
For active power, only the dissipation factor must be known accurately since loss current in Z, adds directly to the in-phase current I,. For reactive power, the capacitance also must be known and the temperature coefficient of capacitance for the polystyrene units is approximately 100 ppm/"C. This limits the accuracy of reactive power measurements made using this bridge. Capacitor calibra-  tions at the required accuracy level are not available routinely at NBS. Thus a scheme is being developed for intercomparing all four capacitors to a well-characterized l-nF gas-dielectric capacitor. The uncertainty of measurements to date (for both capacitance and dissipation factor) are given in Table I. The test current I , is scaled to 100 mA in a two-stage current transformer, T,. The primary winding, N,, is 20 turns tapped for 0.5-, 1-, 2 . 5 , 5 , and 10-A input currents. The 100-turn secondary and tertiary windings ( N 6  and N 7 ) provide the 100-mA secondary and error currents to T3. A current transformer of similar design has been shown to have in-phase and quadrature errors of less than 15 ppm from 50 Hz-10 kHz. Estimates of the in-phase and quadrature errors over the full frequency range are given in Table I.
This scaled-down version of test current is compared to the reference currents, ZI and Z, in current comparator T3.
Nominally, the 100-mA current in the one-turn winding N8 (N9 carries only a small error current) is balanced against the l-mA reference current in 100-turn windings Nlo and/or NI I . At unity power factor with Zl = 1 mA and 1, = 0, the current comparator will balance if the test current is in phase with the test voltage and has the appro-priate magnitude to produce 100 mA in N8. At zero power factor with ZI = 0 and Z, = 1 mA, balance is obtained when 1, is connected to N l o (using switch SI) and the current leads the voltage by go", or when Z, is connected to NI and the current lags the voltage by 90". At other power factors a combination of Zl and 1, produces a 1-mA current with the appropriate phase angle to balance the test current. Balance is achieved by adjusting I, Zl, and Z2 to null the detector connected across the detection winding NI?.
The variable capacitor C, is used to tune NI2 for resonance. Balance may be done manually, remotely under computer control, or automatically by closing switch S, which drives the voltage across NI, to zero by amplifying the imbalance signal in A , and feeding it back through the transconductance amplifier AI. The latter effectively forces I to track I/, thus eliminating any instability in the current channel.
To maintain low input impedances of the windings Nlo and NI I and to minimize their interwinding capacitances, the number of turns was limited to 100 in each winding.
Assuming a nominal value of 1 mA for ZI, 1-ppm resolution requires the detection of 1-or 100-nA turns. Sensitivity depends on the number of turns in the detection winding, NI*, the permeability and dimensions of the core, and the operating frequency. An obvious means for increasing the sensitivity is to increase the number of turns in the detection winding. However, this reduces the frequency range by lowering the self-resonant frequency due to the increased interwinding capacitance.
In view of the above considerations, two current comparators were selected with a crossover frequency at 1 kHz. The low-frequency unit has a toroidal core with 1100 turns in the detection winding while the high-frequency unit has a smaller core with 200 detection winding turns. Both current comparators have magnetically shielded sensing cores and two-stage (compensated current com-parator-type) construction as described in,[ 101. The measured in-phase and quadrature errors are given in Table I.
Additional current pumps are needed to ensure that the currents in Nlo and NI I are strictly a function of the BIVD output voltages and the impedances R and C. Amplifiers A4 and A5 supply the current for lead and winding impedances between the terminals of R and C and ground, minimizing the influence of these impedances on ZI and Z2 [ 1 11. The degradation of these pumps with frequency is included in the impedance errors given in Table I.
At balance the test current Z for leading power factor is given by lN8) ( N 6 / N 5 ) (1) and the apparent power is expressed in terms of the active power P and the reactive power Q by where VI = vrV,/N2.

ERROR ANALYSIS
The various sources of in-phase and quadrature error and their estimated uncertainties are listed in Table I.
The root-sum-square of the components which influence P and Q are given as coefficients A , B , C, and D in Table I. The associated uncertainties U, and U, may be expressed in terms of these coefficients and the phase angle 0 between the test voltage and current: U, = [ A~ cos2 6 + B~ sin2 U, = [c' sin2 6 + o2 cos2 6 1 "~. ings, IV. SUMMARY AND CONCLUSIONS Design considerations and preliminary experimental results have been described for an audio-frequency power bridge which is still undergoing system-based evaluation. Principal components have been constructed, and tested, and their error limits established. Work is still in progress to characterize the system, particularly above 1 kHz. At power frequencies, system uncertainties of less than 20 ppm are comparable with the earlier power-frequency bridge [2]. The main difference is that the earlier bridge operated with smaller reference currents, permitting the use of stable low-loss, gas-dielectric capacitors. The higher value solid-dielectric capacitors must supply the larger reference currents needed for the broad-band current comparators in the new bridge.
The use of a current comparator-based power bridge for basic realization of ac power at the conventional power frequencies of 50-60 Hz is a well established technology capable of accuracies in the 10-20 pprn range. The extension of the same technology to audio frequencies is conceptually attractive but not simple in practice. While similar principal components can be used at power as well as audio frequencies, the detailed implementation of these components is such as to restrict their highest accuracy over a relatively narrow band of frequencies. The development of a broad-band system may involve some sacrifice in accuracy, use of more sophisticated components and compensation techniques and, in extreme cases, use of duplicate components for different frequency ranges.
In the iterative process involving design, redesign, and testing of critical components, all of the above realities were encountered. It is entirely unrealistic to expect the ' same high accuracy over the audio-frequency range as that which can be achieved at power frequencies. For scaling voltages, specially designed binary inductive dividers had to be substituted for more conventional and commercially available decade dividers. Two current comparators and two voltage transformers, each designed to cover over a decade of frequencies, were required for the entire frequency range.
, The greatest difficulty encountered was the unavailability of routine calibration capabilities for precision resistance and capacitance elements above power frequencies.
As mentioned earlier, audio-frequency calibrations for impedances R and C are not readily available at the parts per million level, although the state of the art for impedance measurements is considerably better than the figures in Table I imply. Calibration techniques are being developed which make use of the phase linearity of the digital waveform generator, as well as the wide-band accuracy of the BIVD's and the current comparators. It is expected that the relatively large uncertainties presently assigned to R and C may be reduced considerably.
A source of error in all systems is the uncertainty in the ac voltage measurement. 5-ppm uncertainty in the 60-Hz voltage measurement results in a 10-ppm uncertainty in power. Above 1 kHz the TVC accuracy degrades rapidly and more basic measurement techniques using thermal converter standards are required to verify the accuracy of voltage measurements made between 1-20 kHz. Several alternate techniques are being considered which could reduce the voltage uncertainty at higher frequencies to 10 PPm* The design, construction, and evaluation of principal % system components is nearly completed and experimental results to date indicate that the performance goals are attainable. Preliminary power comparisons between this bridge and the earlier power-frequency version were performed using a stable time-division-multiplier wattmeter [13] as a transfer standard. The agreement was within 15 ppm at 60 Hz and 50 ppm at 400 Hz.