EVALUATION OF 100 AMPERE, 100 kHz TRANSCONDUCTANCE AMPLIFIERS

Donald T. Hess and Kenneth K. Clarke

Abstract - This paper presents experimental evaluation of the performance of more than twenty-five production units of a 100 A, dc to 100 kHz transconductance amplifier. In addition to the stability, uncertainty, distortion and frequency response, experimental results seem to indicate that the output impedance may be closely modeled by a parallel combination of a resistor and a capacitor in series with a resistor. This model is then used to estimate, and to correct for, the effect of load inductance on high-frequency, high-current measurements.  

I. INTRODUCTION

A 100 Ampere, dc to 100 kHz transconductance amplifier has been produced and experimental data have been taken on the performance of more than 25 units. The amplifier comprises five decade current ranges from 2 mA to 20 A plus a 100 A range with each range having a compliance voltage of at least 7 V. The five low ranges operate to twice their full scale value. To circumvent the requirement for a very good high current shunt as the output current sampling element on the highest ranges, the design follows the one outlined by Owen Laug [1] by having these ranges generate their output current by combining the output currents of lower current (typically 5 A) current modules. Each of these modules incorporate feedback from a temperature stable (typically less than 1 mW/W/°C), high frequency (1 GHz) shunt which results in gain stability, low distortion and an excellent high frequency response. Nineteen modules are placed in parallel on the 100 A range, ten are placed in parallel on the 20 A range and a single module is employed for the 2 A range. The lower current ranges employ current amplifiers which are similar to the current modules with the exception that their output stages deliver smaller currents.

The transconductance amplifier measures and displays both the compliance voltage and the frequency of the input signal. It also contains an IEEE-488 interface which permits automated reading of these displays as well as automated range setting.

II. AMPLIFIER CHARACTERISTICS

Some of the important properties of such an amplifier are the stability and uncertainty of the transconductances, the distortion, the linearity with output current levels, the output impedance, and the variation of these properties with frequency, compliance voltage and temperature. These characteristics are not unrelated. For example, to maintain the gain within limits as the compliance voltage varies implies that a minimum value for the output impedance of the range in question exists. Unless the distortion is low, the definitions of the other quantities becomes blurred. If variations occur with time, or temperature, then measurements become very difficult.

The total harmonic distortion, THD, measured for all current ranges is less than -70 dB at low frequencies, less than -60 dB at 15 kHz and less than -40 dB at 100 kHz.

For all ranges the linearity is within ±100 ppm of the full scale range value.

III. AMPLIFIER MODEL AND ERROR CORRECTIONS

Based on direct measurements, a very accurate model for the transconductance amplifier, which is valid for each current range with different parameters, has been obtained. In this model, which is shown in Fig.1, V₁ is the input voltage to the amplifier, G is the transconductance, R₀ is the parallel output resistance, C₀ is the parallel output capacitance and R_S is its series loss resistance. For each current range, the value of R₀, the value of G, the value of C₀ and the value of R_S are shown in Table 1. The values shown are an average of a number of measurements. The spread of the values among different units is within ±4%. As the frequency is increased the effect of R₀ becomes negligible compared with the effect of R_S and C₀. For any given frequency, the series combination of C₀ and R_S may be modeled as an equivalent parallel resistor-capacitor combination where the resistor is a decreasing function of frequency.

Figure 1. Transconductance Amplifier Model

Table 1. Transconductance Amplifier Parameters

On the higher current ranges, the larger capacitance resonates with the inherent inductance (typically between 40 nH and 200 nH) in series with the load at a low enough frequency to affect the output current. In particular, the load current becomes the circulating current of a tuned circuit and is thus larger than the generated output current of the amplifier. Figure 2 illustrates this situation. For the circuit of Fig. 2, the ratio of the current flowing through the load, I_L, to the input voltage, V₁, given by

where w is the radian operating frequency, R_L is the load resistance and L is the inductance of the load and its interconnections. It is apparent that at low frequencies the ratio reduces to the transconductance while at higher frequencies the ratio becomes the effective transconductance which increases with frequency. For small deviations from the low frequency transconductance, the increase is almost directly proportional to w², to L and to C₀.

Figure 2. Output Circuit Including Load Inductance.

The calculation of the effective transconductance requires the value of the inductance. An expression for L in terms of the measured compliance voltage, V_C (Fig. 2), is given by

where R_L is the low frequency ratio of the measured compliance voltage to the load current which is equal to GV₁. (The transconductance amplifier has a meter which indicates compliance voltage directly.) To obtain the greatest accuracy for L, (2) should be evaluated for the highest frequency of operation, typically 100kHz. Since the value of I_L, which can be determined from (1), is also a function of L, a more complicated quadratic expression for L, which depends only on circuit constants, can be obtained by combining the two equations. An easier approach is to assume that I_L is equal to its low frequency value of GV₁ and to evaluate L from (2). Using this value, I_L can be evaluated from (1) and used with (2) to refine the calculation of L. This procedure usually converges in one or two cycles. Once L is obtained, (1) yields the effective transconductance.

Table 2 presents the compliance voltage, the measured transformer output, the calculated transformer output and the difference between the two vs. frequency.

Tracking of the measured and the calculated output at the 100A level to better than 700 uV/V from 30 kHz to 100 kHz has been realized.

Table 2. Comparison of Measured and Calculated Results at 100 A

In the cases where two series-connected current measuring devices are being compared with each other, the accuracy requirement disappears. In this case, the effective transconductance merely lets the user have a good idea of the actual current level through the devices as a rough check on the device being used as the reference.

In testing the transconductance amplifiers, extensive use is made of computer controlled instrumentation. This allows easy correction for variations of input voltage with frequency and allows the mechanization of (1) and (2) so that results are obtained without the need of further calculation.

Table 3. Comparison of Measured and Calculated Results with Variations in Load Inductance

IV. CONCLUSION

The experimental evaluation of the characteristics of a number of wide-band, high current transconductance amplifiers has been presented. In addition, a method for accurately calculating the output current at high frequencies when a significant amount of series inductance is present in series with the load has been outlined. Such an amplifier, with its low measured uncertainties, should provide a valuable tool for creating and evaluating current sensing artifacts which extend to 100 A and 100 kHz. (National laboratory certification to the 20 A, 100 kHz level only became available in 1997 [2].)

REFERENCES

[1] O.B. Laug, "A 100 A, 100 kHz Transconductance Amplifier", IEEE Trans. Instrum. Meas., vol 45, pp 440-444, June 1996