A voltage-controlled resistor for the remote control of monostable multivibrators

M. J. ChudobiakAvtech Electrosystems Ltd., PO Box 5120, Stn. F, Ottawa, Ontario, Canada K2C 3H4
Abstract
A new method is introduced for generating a precise large-signal voltage-controlled resistance for the purpose of remotely controlling monostable multivibrators (one-shots). The circuit presented offers linear control of the resistance with ten to one resistance variation and infinite resolution, and a usable resistance range of approximately 100 to 500 k. The full-scale resistance can be arbitrarily set within this range. The circuit has a bandwidth of 10 MHz, and the voltage across the resistance can be as large as ±12 Volts. The voltage-controlled resistance is generated by using an analog voltage-controlled current source.
I. Introduction
Monostable multivibrators, or one-shots, are used extensively in instrumentation to introduce variable delays or to control signal pulse widths. Many excellent low-jitter one-shots are commercially available in monolithic IC form. The timing characteristics of these one-shots are almost always controlled by a resistor and a capacitor network. Typically, if the capacitor is fixed, varying the resistance over a decade range will allow decade control of the output pulse width.
Unfortunately, this arrangement does not lend itself easily to remote or computer control. The resistance must remain very close to the one-shot to eliminate wire inductance, particularly in high-speed circuits. For this reason, it is of interest to have a resistance that can be controlled by a DC voltage, or by a digital word, both of which can be transmitted over large distances for remote control. Several manufacturers have introduced digitally controlled resistors, such as the Dallas Semiconductor DS1267 and the Xicor 93XX series. However, these devices have limited resolution. The DS1267 has 256 resistance steps [1], and the Xicor 93XX has only 99 [2]. This is inadequate for many purposes. Also, these devices are available with only a few full-scale resistances and with a ±20% resistance tolerance, and are intended to operate between -5V and +5V. These products do not specify a maximum bandwidth, since they are intended primarily for low-frequency control applications.
Field-effect transistors have long been used as voltage-controlled resistors [3] and are often cited in textbooks [4], but they have several undesirable properties. For good linearity (i.e. RDS independant of VDS) the signal voltage VDS is restricted to VDS << VGS - VT, which in practice limits the voltage across the resistance to several hundred millivolts. Since the voltage across a one-shot timing resistor can be 5V, this is insufficient. Also, RDS is inversely proportional to VGS - VT. It is more convenient to have a resistance that is directly proportional to the control voltage. Furthermore, the FETs that are designed specifically for use as voltage-controlled resistors have rather poor tolerances. For instance, the Siliconix VCR4N is specified as having a minimum RDS at a given VGS and ID of between 200 to 600, a three to one range [5].
This paper introduces an analog voltage-controlled resistor (VCR) which allows decade variation of the resistance, with infinite resolution and 10 MHz bandwidth. The effective resistance is directly proportional to the control voltage, and signal voltages of up to ±12 Volts can be accomodated. It accomplishes this by using an analog divider acting as a voltage-controlled current source.
II. The voltage-controlled current source
Figure 1 shows the circuit for a conventional passive resistor, and the circuit model that has been used to implement an electronically controllable active resistance. This second circuit is designed so that the output current on terminal 2 is equal to V12/Reff, where Reff is the effective resistance. (It is an effective resistance in the sense that it is not due to any physical resistance present in the circuit.) This effective resistance is only present at terminal 2; looking into terminal 1 one sees an open circuit. The fact that the current into terminal 1 is not equal to the current leaving terminal 2 does not affect the effective resistance if the source impedance at terminal 1 is zero. This is the case in most one-shots, where one of the resistor terminals is connected to a constant-voltage source, which by definition has zero output impedance for the ideal case. The output current is supplied by a power supply at terminal 3.

Figure 1. Circuit models for a conventional passive resistor and an active resistor.


Figure 2. Timing Circuit for The 74221 One-Shot
The timing circuit for one half of a 74221 dual one-shot is shown in Figure 2. The timing resistor is connected between the Vcc power supply and the R/C terminal on the one-shot. The resistor can be replaced with the current source shown in Figure 1 if it has the transfer function:
(1)
where VR is the voltage between Vcc and the R/C terminal. To achieve linear control of the effective resistance, a second control voltage is needed such that:
(2)
where Vcon is an externally applied control voltage, and m is a proportionality constant.


Figure 3 - Voltage-Controlled Resistor Circuit and One-Shot. (Power supplies are shown for the AD734 only.)

Equation (2) can be implemented by the AD734 analog divider. The voltage controlled current source circuit is shown in Figure 3. The AD734 with the resistor RS implements the function [6]:
(3)
The 50 k term is due to the finite input impedance of the Z1 input. If Y1 = Vcc, and Y2 is equal to the voltage at the R/C terminal of the one-shot, as shown, then (3) has the form of equation (2) with
(4)
(5)
(6)
Hence, using (1), (2), (5) and (6),
(7)
If one assumes that RS << 50 k, then
(8)
The op amp OP2 in Figure 3 serves to introduce an offset, such that
(9)
Then one can write
(10)
where
(11)
and
(12)
This offset allows the control voltage to range between zero and some maximum voltage while establishing a minimum effective resistance. (All one-shots have a minimum timing resistance rating.) Also, the AD734 requires that for proper operation, |X1-X2| < 1.25 (U1-U2). The voltage offset introduced by the op amp can be used to ensure that this condition is satisfied. (U1-U2 must be positive, since the npn transistor in the AD734 U input will support current in only one direction. The X, Y and Z inputs will support either polarity.)
The buffer BUF1 ensures that the finite input impedance of the Y2 and Z2 terminals does not influence Reff. BUF1 has an input impedance of RBUF = 5 M such that RBUF >> Reff and IBUF << Iout, so Iout = IRC to a high degree of accuracy. Linearity is degraded if BUF1 is removed.
Experimental Results
The circuit of Figure 3 was constructed with the following circuit parameters: RS = 1.5 k, R1 = 1 k, R2 = 900 , R3 = 13.5 k, X1 = 0 V, X2 = -1.00 V, and Vos = 15 V. For these values, Rmin = 1.5 k and = 1.35 k/V. With these parameters, the effective resistance should vary linearly from 1.5 k to 15 k as the input voltage Vin is varied from 0 V to +10 V.
The output pulse width of the 74221 is PW = Reff C ln 2, so choosing C = 0.01 F will result in a pulse width range of approximately 10 s to 100 s. Figure 4 shows the measured output pulse widths as a function of the input control voltage. As expected, the output varies linearly over the desired decade range. For comparision purposes, Figure 5 shows the measured output pulse widths when fixed carbon-composition resistors were used. Comparing the two curves, it is evident that the effective resistance of the VCR does indeed vary between 1.5 k and 15 k, and that pulse width control is not degraded by using an effective resistance.
Figure 4 - Pulse width control using the voltage-controlled current source as the resistive element.

Figure 5 - Pulse width control using fixed carbon-composition resistors as the resistive elements.
IV. Limitations
The voltage-controlled resistor (VCR) introduced above has several limitations. Most importantly, it is only useful in applications where one of the resistor terminals is connected to a voltage source with zero output impedance. This is due to the fact that only terminal 2 of the VCR has a current flow commensurate with the voltage across the resistance. However since the voltage at a source with zero output impedance is independant of the current, this does not affect the effective resistance. This is not a limitation in most one-shot applications, but does restrict its use elsewhere.
The AD734 has a small-signal bandwidth of 10 MHz, and its output stage has a slew rate of 450 V/s. This is sufficient to provide linear operation over the entire pulse width range of the 74221 one-shot. The buffer BUF1 must exceed these values for high-speed operation. The LM6321 has a bandwidth of 50 MHz and a slew rate of 800 V/s. This bandwidth limit refers to Reff and to the X, Y and Z inputs. Op amps with much lower bandwidths were used on the U inputs, since Vin is typically a DC, or slowly varying, control voltage. However, if faster op amps are used the circuit can be used as a high-speed pulse-width modulator. This application is problematic when FET-based resistors are used, since the input capacitance of FETs will present a low input impedance to a high-frequency control signal, and may also result in signal feedthrough [7].
The W output of the AD734 can typically supply a maximum of 50 mA of current, which limits the minimum effective resistance. For instance, for a 5 V output signal, the minimum Reff is 5 V/ 50 mA, or 100 . (If a voltage buffer is added to the W output, Reff will be determined by the output current rating of the buffer, so lower resistances can be achieved.) However, since the W output can not provide more than ±12V, the voltage drop across RS must be small enough to allow the full output signal to be developed. For instance, for a 5V output signal, IoutRS can not exceed 12V - 5V, or 7V. The maximum value of Reff is limited by the input impedance of the buffer BUF1. For good linearity, Reff < 0.1 RBUF, so Reff should not exceed 500 k. Within these restrictions, Rmin and can be set arbitrarily. The X, Y, and Z inputs and the W output on the AD734 will operate at voltages between -12V and +12V, so higher voltages can be used than in the case of a digital resistor, and much higher than in the case of a FET. The X, Y and Z inputs have offset voltages of roughly 20 mV, which limits the minimum input voltage, and hence the maximum variation of the effective resistance. However, the effective resistance can be varied over at least two decades.
The design accuracy of Reff is primarily set by the tolerances of the resistors R1, R2, R3, and RS, since the division accuracy of the AD734 is typically 1%. This is significantly better than what can be achieved using commercially available digitally programmable resistors or FETs.
V. Conclusions
A large-signal voltage-controlled resistor has been introduced. This resistor has been implemented using a voltage-controlled current source, and offers significant improvements over previous methods of generating voltage-controlled resistance, including higher precision, larger operating voltages, infinite resolution, 10 MHz bandwidth, and arbitrary full-scale resistance. For the circuited presented here, the resistance is directly proportional to the control voltage and variable over a ten to one range. This flexible circuit has proven to be useful in the remote control of timing circuits and delay generators, and should be useful in a variety of other applications as well.

References
[1] 1990-1991 Product Data Book (Dallas Semiconductor, Dallas, 1990), p. 750.
[2] 1992 Data Book (Xicor, Milpitas, Ca., 1992), p. 4-1.
[3] W. Gosling, Brit. Communications and Electronics 11, 856 (1964).
[4] P. Horowitz and W. Hill, The Art of Electronics, 2nd ed. (Cambridge Univ. Press, Cambridge, 1989), p. 138.
[5] Low Power Discretes Data Book (Siliconix, Santa Clara, Ca., 1991), p. 4-85.
[6] Special Linear Reference Manual (Analog Devices, Norwood, Ma., 1992), p.2-55.
[7] W. Gosling, W. G. Townsend, and J. Watson, Field-Effect Transistors (Butterworths, London, 1971), p. 232.