## WIDEBAND AMPLIFIERS

When analyzing amplifiers mathematically, it is convenient to assume that the gain calculations are not affected by the reactive elements that might be present in the circuit. How­ever, in reality, capacitances and inductances play a major role in determining how the amplifier performs over a range of frequencies. The effect of inductances can be minimized but it is impossible to ignore the presence of capacitances. This effect is more pronounced particularly while analyzing multistage amplifiers. Coupling capacitors and bypass capaci­tors can reduce the gain of an amplifier at lower or higher frequencies, because the capacitive reactance is inversely pro­portional to the frequency. In other words, as the frequency increases, the capacitive reactance decreases because

1

x =

j(2n fC)

Therefore, if there is a grounded bypass capacitor, signal cur­rents may be inadvertently diverted to ground instead of be­ing transmitted to the output. This is because bypass capaci­tors offer low reactances to signal currents at higher frequencies. However, the bypass capacitors offer high re­actances to signals at lower frequencies, and therefore diver­sion of such currents to ground does not pose a major problem.

Figure 1 is a representation of a frequency plot of an am­plifier. Here, the output voltage or power gain is plotted against a range of frequencies (for a given constant input volt­age). The frequency axis is normally plotted on a logarithmic scale. The unit for the y axis is decibels (dB); the number of decibels of gain is given by

201ogi° ^

or

Table 1. Bandwidth Values for Selected Electronic Signals

 Signal Type Frequency Range Electrocardiograms 0.05 to 100 Hz Audio signals (human ear) 20 Hz to 15,000 Hz AM radio waves 550 kHz to 1600 kHz FM radio waves 88 MHz to 100 MHz Microwave and satellite signals 1 GHz to 50 GHz

amplifier characteristic be assigned a voltage level of Vflat. Then the frequencies at which voltage levels have dropped to

0. 707Vflat are denoted by fL and fH. The range of frequencies that lies between f L and f H is known as the bandwidth. In other words, the bandwidth can be defined as the frequency range over which the amplifier gain remains within 29.3% of its maximum value (3 dB level, or 1 — 0.707 = 0.293).

The bandwidth of an amplifier depends upon the applica­tions and signal type involved. Bandwidth values for some selected electronic signals are given in Table 1.

## MANUFACTURERS

High-Precision Instruments for Voltage Standards

• Datron Systems Division, 200 West Los Angeles Ave., Simi Valley, CA 93065-1650. Phone: 805-584-1717. Fax: 805-526-0885.

• The Eppley Laboratory, Inc., 12 Sheffield Avenue, New­port, RI 02840. Phone: 401-847-1020. Fax: 401-847-1031.

• Fluke Corporation, MS 250, P. O. Box 9090, Everett, WA 98206-9090. Phone: 800-44F-LUKE or 425-347-6100. Fax: 425-356-5116.

• Hewlett Packard Co., Electronic Measurement Systems, 815 14th Street SW, P. O. Box 301, Loveland, CO 80538. Phone: 970-679-5000. Fax: 970-679-5954.

• Julie Research Laboratories, Inc., 508 West 26th Street, New York, NY 10001. Phone: 212-633-6625. Fax: 212­691-3320.

• Keithley Instruments, 28775 Aurora Road, Cleveland, OH 44139. Phone: 800-552-1115 or 440-248-0400. Fax: 440-248-6168.

Voltage Reference Integrated Circuits

• Analog Devices Inc., 1 Technology Way, P. O. Box 9106, Norwood, MA 02062-9106. Phone: 781-329-4700. Fax: 781-326-8703.

• Burr Brown Corp., International Airport Industrial Park, 6730 South Tucson Boulevard, P. O. Box 11400, Tucson, AZ 85734. Phone: 800-548-6132 or 520-746-1111. Fax: 520-889-1510.

• LTC (Linear Technology Corp.), 1630 McCarthy Boule­vard, Milpitas, CA 95035-7417. Phone: 408-432-1900. Fax: 408-434-0507.

• Maxim Integrated Products, 120 San Gabriel Drive, Sun­nyvale, CA 94086-9892. Phone: 408-737-7600. Fax: 408­737-7194.

• NSC (National Semiconductor Corp.), MS D2565, 2900 Semiconductor Drive, Santa Clara, CA 95051. Phone: 408-721-8165 or 800-272-9959. Fax: 800-737-7018.

• Thaler Corp., 2015 North Forbes #109, Tucson, AZ 85745. Phone: 800-827-6006 or 520-882-4000. Fax: 520­770-9222.

## IMPEDANCE TOMOGRAPHY

This is a technically advanced approach whereby the imag­ing of an object is realized from measurements in multiple directions. Usually, 16 to 32 electrodes are placed equidis­tantly in a plane around the patients. This yields anatomi­cal slices or sections, which can be viewed from various an­gles. Reasonably good soft tissue contrast can be achieved by impedance imaging, because of the different electrical resistivities of the various tissues. Impedance images are inferior to alternative techniques such as computed tomog­raphy and magnetic resonance imaging (MRI). Due to the three-dimensional spread of current into the object, the slice thickness cannot be confined to 1 mm or 2 mm. The strength of impedance tomography, however, resides in its functional imaging capabilities. Functional imaging is pos­sible if variations in tissue resistivity are associated with particular physiological events. The first in vivo impedance tomography images were produced in 1983 at the Univer­sity of Sheffield, and the theoretical background as well as illustration have been summarized by (53). A newer ex­ample has already been mentioned, when the right atrium was selected as the region of interest, and compared with results from MRI. (21) noninvasively assessed right ven­tricular diastolic function in patients with chronic obstruc­tive pulmonary disease and in controls by means of region of interest analysis applied to electrical impedance tomog­raphy. Comparison with MRI data showed a correlation of r = 0.78 (n = 15), while pulmonary artery pressure (mea­sured by right-sided heart catheterization) yielded an ex­ponential relationship with r = 0.83 (p < .001). The same authors (29) also improved cardiac imaging in electrical impedance tomography by means of a new electrode con­figuration, whereby the traditional transversal positioning at the level of the fourth intercostal space on the anterior side was replaced by attachment at an oblique plane at the level of the ictus cordis anteriorly and 10 cm higher pos­teriorly. Comparison with MRI findings gave good results (Fig. 6), while the reproducibility coefficient was 0.98 at rest and 0.85 during exercise.

 Figure 7. Cole-Cole diagram for an impedance with a single time constant.

## PRECISION MEASUREMENTS

In classical metrology, one uses a precision (six-digit, seven­digit, or eight-digit) voltage divider, known as a potentio­meter. This has very little in common with the variable resis­tor often called a “potentiometer” or ‘‘pot’’—but it does act as a voltage divider. When such a precision potentiometer is used with a null meter, any voltage can be compared with a standard or reference voltage. The unknown voltage is thus well determined, according to the ratio of the potentiometer and the standard voltage (allowing for its uncertainty.) How­ever, most precision potentiometers are not guaranteed to maintain their linearity to 1 LSD (Least Significant Digit) for long-term accuracy, after their resistive dividers are trimmed and calibrated. A good potentiometer may hold better than 1 X 10—6 linearity per year, but it is not guaranteed that switching from 0.499999 to 0.500000 will not cause a decrease of its output. Further, an inexperienced user may find it very time-consuming to use such a divider. When taking a large number of data, long-term system drift may cause errors that could be avoided by taking data more quickly.

The author’s recommendation is to use a good six-digit or seven-digit multislope integrating digital voltmeter (DVM), with 1 X 10—6 inherent differential linearity and excellent overall (end-to-end) linearity. The author has had excellent experience with HP 3456, 3457, 3468, and other similar inte­grating voltmeters. Differential nonlinearity has never been observed to exceed 1 X 10—6 of full scale, on 10 V scales. Noise, offsets, and gain errors are usually acceptably small. For best absolute accuracy, the DVM’s full-scale factor should be com­pared with other stable references. Note that not all six-digit or seven-digit DVMs have this inherent linearity.

CONCLUSION

Since most advances in references are designed by IC manu­facturers on a commercial basis, to be aware of good new products, one must inquire of the IC manufacturers, to see what is available. A list of IC makers is provided here, as well as a list of companies making precision references and measuring equipment.

## THE JOSEPHSON JUNCTION

As early as 1972, the advent of the ac Josephson junction promised to provide improved accuracy in its representation of the volt standard. When microwave energy at a precisely known frequency is injected into a stacked assembly of Jo – sephson junctions, held at 4 K by liquid helium, it is possible to generate a voltage that is accurate and stable to better than 0.1 JU. V/V, both theoretically and in practice (36).

Preliminary research confirmed that even the best Weston saturated standard cells had unexplained drifts and noises, of the order of 1 X 10—6, which the Josephson junctions did not. As the Josephson junction equipment became more reliable and easier to operate, it became obvious that they would soon make possible a new, more stable standard. After a consider­able amount of engineering and development, a new represen­tation of the volt was established. The Josephson constant KJ-90, adopted on January 1, 1990, was defined as 483,597.900 GHz/V, exactly.

The ac Josephson junction equipment for establishing ul – traprecise voltage references has typically a precisely known 72 GHz input frequency, and an output of 2.0678336 ^V/GHz. The output of each junction is about 149 ^V. To provide an output at a convenient level, an array of 2000 Josephson junc­tions is integrated, stacked in series, and enclosed in the cryo­genic (4 K) microwave-stimulated chamber, thus providing an output of perhaps 298 mV. This voltage is compared with the 1.018 V level using conventional potentiometric techniques, to calibrate the standard cells that act as secondary transfer references. Equipment to implement this stable reference tends to cost in the vicinity of \$100,000, plus considerable la­bor and operational costs.

Thus on January 1, 1990, the magnitude of the US volt (as well the voltage standards in most other countries) was changed. The new 1990 US volt was established as +9.264 jU, V/V larger than the previous (1972) US standard. Since 1990, the international standard volt has still been defined as

1 W/1 A, but the standard representation of the volt is the output of the Josephson junction apparatus.

THE AMPERE

In theory, the volt is not an absolute standard. The volt has long been defined as the potential such that 1V X 1 A = 1 W. In turn the ampere is defined as an absolute standard, such that 1 A flowing through a pair of very long wires (of negligible diameter), separated by 1 m, will cause a force of

2 X 10—7 N per meter of length. In practice, the volt is a much more useful and usable standard. The ampere standard is not very portable. In fact, when a 1 A standard is required, it is normally constructed by establishing 1 V and 1 П, causing 1 A to flow.

THE OHM

In theory, the ohm is not an absolute standard, but the ratio 1 V/1 A, with the volt and ampere defined as above. As of 1990, the representation of the ohm was redefined using the quantum Hall effect (QHE), discovered by Klaus von Klitz – ing (37):

The QHE is characteristic of certain high-mobility semiconductor devices of standard Hall-bar geometry, placed in a large applied magnetic field and cooled to a temperature near one kelvin. For a fixed current I through a QHE device there are regions in the curve of Hall voltage vs. gate voltage, or of Hall voltage vs mag­netic field depending on the device, where the Hall voltage UH remains constant as the gate voltage or magnetic field is varied. These regions of constant Hall voltage are termed Hall plateaus. Under the proper experimental conditions, the quantized Hall re­sistance of the ith plateau RH(I), defined as the quotient of the ith plateau to the current I, is given by

RH(i) = UH (i)/I = RK/i

where i is an integer and RK is now termed the von Klitzing con­stant after the discoverer of the QHE….

Numerically, RK is about 25,813 ohms. The value agreed upon as an international constant was RK.90 = 25,812.807 ohms.

This was a considerable improvement, as the best older stan­dard resistors were shown to be drifting at about —0.1 ^П/П per year. With the quantum standard, such drifts are ban­ished.