## Design Philosphy of Vector Impedance Meters

The operation of both vector impedance meters is based directly upon the fundamental definition of Impedance

In the simplified block diagram of a typical vector impedance meter, a broadband oscillator applies a CW signal to an amplifier whose output may be leveled. The AC signal from the amplifier passes through the unknown Impedance mounted across terminals A and B. Current flows from the B terminal through the ammeter to ground. Thus, the current through the unknown Is sensed by the ammeter and used to generate an AGC signal which levels the output of the amplifier. The purpose of the AGC loop Is to hold the current constant through the unknown. Since Z = E/l, and I is a constant, Z Is directly proportional to the voltage across the unknown. A high-Impedance broadband voltmeter across terminals A and B can be calibrated to read impedance directly.

To determine the phase angle between the voltage and current, the AC outputs from the voltmeter and ammeter

are fed to a phase detector which is calibrated directly in phase angle.

From the preceding discussion, it is obvious that it is Immaterial whether voltage is held constant or whether current is held constant, so long as one of the two param eters Is held constant. Also the voltmeter, ammeter and phase meter portions of the circuit may either be broadband, or may be track-tuned to the excitation oscillator frequency. Third, the connection to the ammeter at terminal B may be either a direct connection or Inductively coupled.

Probe. Because operating frequencies of the -hp- Model 4815A are high, the current can be monitored with a toroid current transformer in a probe. In addition to the toroid current transformer, the probe contains both the voltage and current channel samplers, a coaxial delay line and the RF test signal injection lead which feeds through the center of the toroid to the probe tip, and is actually the current transformer primary.

The voltage appearing across the unknown is taken from the probe tip through the delay line to the voltage sampler. The current measurement is taken from the secondary of the toroid current transformer.

Voltage and current are sampled at different instants in real time to avoid crosstalk in the measuring channels. The delay line in the voltage channel compensates for the phase difference due to the sampling time difference, thus preserving phase information.

Samplers. Synchronous sampling techniques are used to convert the RF to constant IF frequency signals in the probe. Sampler theory and sampler characteristics have been discussed in previous articles.12 In this instrument, the samplers used for both channels are identical. The IF is 5 kHz with sampling rate controlled with a phase

I Gerry Alonzo, 'Considerations in the Design of Sampling-Based Phase-Lock Loops,' WESCON 1966, Technical Papers 23/2.

' Fritz K. Weinert, 'The RF Vector Voltmeter,' 'Hewlett-Packard Journal,' Vol. 17, No. 9, May 1966, p. 2.

lock loop. By phase comparison of the IF to a reference, a voltage is derived that controls the frequency of a voltage-tuned oscillator in the phase lock loop. Fast pulses for operation of the samplers are produced by a sampler pulse generator synchronized with the voltage-tuned oscillator.

IF System. Two high-gain, narrow band 5 kHz channels, one voltage and one current, terminate in average detectors. In the -hp- Model 4815A, the current channel

^recorder t outputs mag

fricsröeri outputs I phase J

^recorder t outputs mag fricsröeri outputs I phase J

, TrecorderI

. outputs

, TrecorderI

. outputs

Fig. 6. Both vector impedance meters use the same basic logical arrangement, but the high frequency meter uses synchronous sampling techniques which provide tracked tuning of voltage and current channels to produce the 5 kHz IF frequency.

5 kHz signal is amplified, detected and applied to a modulator to form a closed-loop automatic level control (ALC) that holds the test signal current constant.

By holding the RF test signal current constant, the voltage across the unknown is proportional to impedance magnitude. The 5 kHz voltage channel IF is amplified and detected in a manner similar to the current channel. The detected output is read out on the front-panel meter as 'ohms.' The single-frequency IF system makes possible very high Q measurements.

Signals from both the voltage and current channels are limited to remove amplitude variations. They are then applied to a binary phase detector whose output is read on the front-panel phase meter.

### Applications of Vector Impedance Meters

Both vector impedance meters can make a wide variety of measurements. Many components can be measured using either instrument. However due to the difference in frequency coverage and circuit configuration, certain measurements must be performed with the instrument designed for that purpose.

The high-frequency RF Vector Impedance Meter with its probe for in-circuit measurements can be used for measurement of both active and passive devices and circuits. The low frequency Model 4800A is generally limited to measurements of passive components, but with blocking capacitors, may be used to make measurements in circuits with dc present. It can measure active circuits so long as the phase angle is 90° or less and the power supply for the circuit is isolated from the instrument.

### Inductance and Capacitance

Both instruments can be used to determine inductance or capacitance of discrete components. Components may be attached directly to the front panel terminals of the -hp- Model 4800A, or to the component mounting adapter attached to the probe of the -hp- Model 4815 A, Fig. 7. Impedance is measured directly in terms of polar coordinates Z and phase angle 9. Using simple trigonometric relationships, the polar coordinates can be converted into rectangular form where the horizontal component of Z is resistance and the vertical component is inductive or capacitive reactance.

Measuring Q

Low Q components. For a low Q component, that is less than 10, simply determine the phase angle and refer to a table of tangents, since:

High Q components. By adding the necessary resonating element, the Af method may be used to calculate Qs greater than 10. For either parallel or series resonance:

Q = fo/Af where f„ is the resonant frequency and Af is the bandwidth. f„ is the frequency where ZZ is zero degrees. The bandwidth Af is the numerical difference between the frequency above resonance (f2) where ZZ is — or +45°, and the frequency below resonance (f,) where ZZ is + or -45°.

When calculating the Q of small inductors the effect of stray inductance Ls in series with the resonating capacitance, Fig. 8, is included by altering the Af equation to Q s (f0/Af) [1/(1 + Ls/L)].

Another method, called frequency ranging Compares the impedance of the circuit at resonance to its impedance when it is not at resonance. If \Z\t is the impedance of the circuit at resonance (f0) and Z!:, is the impedance of the circuit at 0.1 f„ or 10 f„ then

10|Z|3 ToiZI

for parallel resonance, and for series resonance.

This method will not work for crystals, resonant lines and similar devices.

High Q circuits. The Q of high Q circuits, that is greater than 10, can be calculated by either the Af or the frequency ranging methods.

Low Q circuits. When circuit Q is less than 10, the Q is still accurately calculated by the Af method provided that the loss is in shunt in a parallel resonant circuit or in series in a series resonant circuit. In parallel resonant circuits where the loss can be assumed primarily in series with the inductor, Fig. 8, a modified form of the Af method calculates Q accurate to ±0.5 for all Q with the formula:

where f0 is the frequency at 0° phase angle and fL> is the frequency at —45° phase angle. The Q calculated is for frequency f0.

### Crystal Resonance

A crystal may be represented by the equivalent circuit, Fig. 9(a). This circuit exhibits a series and parallel resonance very close together in frequency, Fig. 9(b), with the series resonance occurring at the lower of the two frequencies.

Crystal resonance may be easily measured with the -hp- 4815 RF Vector Impedance Meter. Series resistance Rs may be read directly by tuning to series resonance and reading impedance directly. For more accurate frequency measurements, an electronic counter may be driven from the front panel RF output terminal.

From a plot of impedance versus frequency, it is possible to determine the capacitive reactance needed to pull the crystal frequency to some desired value. It also is possible to calculate the sensitivity of the pulled frequency to changes in the pulling capacitance. Besides crystal capacitance and inductance, Q may also be determined.

Since crystal Q may be very high (up to 2 million for natural quartz), it is generally desirable to use a counter for frequency measurement. For Q greater than 100,000, a high-accuracy, high-resolution frequency source such as a frequency synthesizer is desirable.

Fig. 8. All losses associated with a Q measuring circuit should be considered when measuring Q of a small inductor. The stray in ductance Ls of the resonating capacitor C and the resistive losses R of the inductor L are shown.

Cs ne

Fig. 9. Each resonance of a crystal may be represented with the equivalent circuit (a). All crystals exhibit a tow impedance series resonance and a high impedance parallel resonance (b), very close together in frequency, with the series resonance at the lower of the two frequencies.

Parallel resonance

Series resonance

Parallel resonance

Series resonance

Transformer Measurements

One of the more sophisticated capabilities of the vector impedance meters is characterizing a transformer, Fig. 10. With the transformer secondary open and the primary connected to the terminals of the instrument, the primary inductance can be measured directly by choosing a frequency range where the phase is between plus 85° and 90°. The copper and core losses in the primary vary with frequency and can be determined at the lowest measurement frequency where the phase angle is 45°, since the inductive reactance is equal to the resistance at this frequency. The resistance is then 0.707 times the impedance, as read on the Z magnitude meter.

Transformer capacitance. Capacitance of the transformer primary can be determined by selecting a measurement frequency at which the primary inductance and capacitance resonate (phase angle of 0°). If this frequency is out of the range of the instrument, an external capacitor of known value can be shunted across the primary. Since the inductance and the frequency are known, the transformer capacitance is the resonating capacitance minus the known shunt capacitance.

Primary-to-secondary capacitance of the transformer can be measured by using one lead each of the primary and secondary as terminals. With the frequency dial set to an appropriate frequency, the capacitance can be read directly. The effectiveness of interwinding shields can be measured by' connecting shields to the ground terminal of the -hp- Model 4800A.

Turns Ratio. To find turns ratio, the equations Zs = n2Zp and n= = Zs/Z„ are used, where n equals the number of secondary turns divided by the number of primary turns. Then, by selecting a frequency where the primary inductance is high with respect to some resistance, say 100 ohms, a 100-ohm resistor plaçed across the secondary will reflect an impedance in the primary. Using the equations, Zs = 100 ohms and Z„ is the reading on the Z magnitude meter. A near zero phase angle reading assures that the Z magnitude meter is reading a reflected resistance and not an inductance in the transformer itself.

Mutual inductance. It is possible to determine mutual inductance of the transformer by measuring its inductance in a series aiding configuration and then in a series opposing configuration. Subtracting the smaller reading

SPECIFICATIONS

-hp-MODEL 4800A VECTOR IMPEDANCE METER

Frequency Characteristics Range: 5 Hz to 500 kHz in five bands: 5 to 50 Hz. 50 to 500 Hz, 0.5 to 5 kHz, 5 to 50 kHz, 50 to 500 kHz.

Accuracy: t 2% from 50 Hz to 500 kHz, ' 4% from 5 to 50 Hz. ± 1% at 15.92 on frequency dial from 159.2 Hz to 159.2 kHz, i:2% at 15.92 Hz. Monitor output: levei: 0.2 volt rms minimum; source impedance: 600 ohms nominal.

Impedance Measurement Characteristics Range: 1 ohm to 10 megohms in seven ranges. 10 ohms, 100 ohms. 1000 ohms. 10K ohms. 100K ohms, 1 megohm, 10 megohms full scale. Accuracy: 15% of reading

Phase Angle Measurement Characteristics Range: 0° ±90° Accuracy: • 6°. Calibration: increments of 5e.

### Direct Inductance Measurement Capabilities

Range: 1 fiH to 100.000H, direct reading at decade multiples of 15.92 Hz. Accuracy: 1 7% of reading for Q greater than 10 from 159.2 Hz to 159.2 kHz; 8% of reading for Q greater than 10 at 15.92 Hz.

Direct Capacitance Measurement Capabilities Range: 0.1 pF to 10,000 jj.F. direct reading at decade multiples of 15.92 Hz. Accuracy: ±7% of reading for D less than 0 1 159.2 Hz to 159.2 kHz. :8% of reading for D less than 0.1 at 15.92 Hz.

Measuring Terminal Signal Characteristics Wave shape: sinusoidal.

Distortion: less than 1% from 10 Hz to 50 kHz, less than 0.3% from 50 Hz to 500 kHz, less than 1.5% from 5 Hz to 10 Hz. Signal level: less than 2.7 mV rms 1 to 1000 ohms, approximately 27 mV rms 10K to 100K ohms, approximately 270 mV rms 100K ohms to 1 megohm, approximately 2.7 V rms 1 megohm to 10 megohms.

Weight: net 24 lbs. (10.8 kg), shipping 30 lbs. (13.5 kg).

Price: $1.490; Option 01. recorder outputs for Z, 0, and frequency $100.

-hP-MODEL 4815A RF VECTOR IMPEDANCE METER

Frequency

Range: 500 kHz to I08 MHz in five bands: 500 kHz lo 1.5 MHz, 1.5 to 4.5 MHz. 4.5 to 14 MHz 14 to 35 MHz. 35 to 108 MHz

1 592 and 15.92 MHz. RF monitor output: 100 mV minimum into 50 ohms. Impedance Magnitude Measurement

Range: 1 ohm to 100K ohms: fult-scale ranges: 10 30. 100, 300, 1K, 3K, 10K, 30K, 100K ohms.

Accuracy: ■> 4% of full scale : 3Q ^ • ■ ^,,1%

of reading, where f frequency in MHz and Z is in ohms; reading includes probo residual impedance.

Calibration: linear meter scale with increments 2% of full scale. Phase Angle Measurement

Range: 0 to 360° in two ranges: 0 ± 90°, 180° ± 90°.

Accuracy: f; (3 + 35^ + 5(fKi,) degrees; where f - frequency in MHz and Z is in ohms. Calibration: increments of 2°. Weight: net 39 lbs. (17,6 kg), shipping 50 lbs. (22,5 kg). Power: 105 to 125 V or 210 to 250 V, 50 to 400 Hz. Price: $2650. Manufacturing Division: ~hp~ Rockaway Division Green Pond Road Rockaway, New Jersey 07866 Prices f.o.b. factory Data subject to change without notice from the larger reading and dividing the result by four yields mutual inductance.

Leakage inductance. To determine leakage inductance of a transformer, the secondary is shorted and the shorting inductance read on the Z magnitude meter. If the leakage reactance is too small to be read directly, a capacitor which will resonate with the leakage inductance may be connected across the primary. The leakage inductance can then be calculated from the known frequency and capacitance.

### Semiconductor Measurements

Dynamic Impedance of Diodes. Both instruments may be used to determine the dynamic impedance of diodes using a known dc current source. (Use blocking capacitors with the low-frequency -hp- Model 4800A.) The impedance of the diode can then be recorded as a function of current. Similarly, by back biasing the diode, the junction capacitance vs. voltage can be measured. Obviously, voltage variable capacitors and current variable inductors can be measured and recorded as a function of voltage and current respectively. Care must be taken to insure that the test signal level does not bias the diodes.

Transistor Measurements. Using a slightly more complicated biasing system than that used for diodes, the input impedance of a transistor can be measured. With the base of the transistor connected to one terminal of the -hp-Model 4800A, and the emitter connected to the other, and the collector connected to the base through a capacitor, Fig. 11(a), the instrument will measure hIb. With the base connected to one terminal, the emitter connected to the other, and the collector connected to the emitter through a capacitor. Fig. 11(b), the instrument will measure hlt.. If the same biasing currents and voltages are used for both the hib and hit, measurements, then from the equation hib hi,.

or h|> can be determined using the relationship:

hu-his

HEWLETT-PACKARD JOURNAL

TECHNICAL INFORMATION FROM THE LABORATORIES OF THE HEWLETT-PACKARD COMPANY

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