AN105

AN105 FETs As Voltage Controlled Resistors Introduction: The Nature of VCRs A voltage-controlled resistor (VCR) may be defined as a three-terminal variable resistor where the resistance value between two of the terminals is controlled by a voltage potential applied to the third. For a junction field-effect transistor (JFET) under certain operating conditions, the resistance of the drain-source channel is a function of the gate-source voltage alone and the JFET will behave as an almost pure ohmic resistor. Maximum drain-source current, IDSS, and minimum resistance rDS(on), will exist when the gate-source voltage is equal to zero volts (VGS = 0). If the gate voltage is increased (negatively for n-channel JFETs and positively for p-channel), the resistance will also increase. When the drain current is reduced to a point where the FET is no longer conductive, the maximum resistance is reached. The voltage at this point is referred to as the pinchoff or cutoff voltage and is symbolized by VGS = VGS(off). Thus the device functions as a voltage- controlled resistor. Figure 1 details typical operating characteristics of an nchannel JFET. Most amplification or switching operations of FETs occur in the constant-current (saturated) region, shown as Region II. A close inspection of Region I (the unsaturated or pre-pinchoff area) reveals that the effective slope indicative of conductance across the channel from drain-to-source is different for each value of gate-source bias voltage. The slope is relatively constant over a range of applied drain voltages, so long as the gate voltage is also constant and the drain voltage is low. Resistance Properties of FETs The unique resistance-controlling properties of FETs can be deduced from Figure 2, which is an expanded-scale plot of the encircled area in the lower left-hand corner of Figure 1. The output characteristics all pass through the origin, near which they become almost straight lines so that the incremental value of channel resistance, rDS, is essentially the same as that of dc resistance, rDS, and is a function of VGS. Figure 2 shows an extension of the operating characteristics into the third quadrant for a typical n-channel JFET. While such devices are normally operated with a positive drain-source voltage, small negative values of VDS are possible. This is because the gate-channel PN junction must be slightly forward-biased before any significant amount of gate current flows. The slope of the VGS bias line is equal to ID/VDS = 1/rDS. This value is controlled by the amount of voltage applied to the gate. Minimum rDS, usually expressed as rDS(on), occurs at VGS = 0 and is dictated by the geometry of the FET. A device with a channel of small cross-sectional area will exhibit a high rDS(on) and a low IDSS. Thus a FET with high IDSS should be chosen where design requirements indicate the need for a low rDS(on). VDS = VGS - VGS(off) ID - Drain Current (mA) Region 1 Ohmic Region Locus Curve Region 2 IDSS VGS = 0 Current Saturation Region VGS t 0 VGS → VGS(off) VP VDS - Drain Source Voltage (V) Figure 1. Typical N Channel JFET Operating Characteristics Updates to this app note may be obtained via facsimile by calling Siliconix FaxBack, 1-408-970-5600. Please request FaxBack document #70598. Siliconix 10-Mar-97 1 AN105 3 ID (mA) 2 –1.5 V 1 –2.5 V –1.5 V 0V ID D G S –400 VGS = –3.0 V –200 200 ID (mA) –3.0 V 5 10 VDS (V) VGS = 0 V Siliconix offers a family of n-channel FETs specifically intended for use as voltage-controlled resistors. These devices have rDS(on) values ranging from 20 W to 4,000 W, where VCR2N = 20 – 60 W, VCR4N = 200 – 600 W, VCR7N = 4 k – 8 kW. Applications for VCRs A simple application of a FET VCR is shown in Figure 4, the circuit for a voltage divider attenuator. –2.5 V VGS = –3.0 V 200 400 VDS (mV) R VIN –2.5 V –1.5 V 0V –200 – + VCR VGS VOUT Figure 2. N Channel JFET Output Characteristics Enlarged Around VDS = 0 V Figure 4. Simple Attenuator Circuit The output voltage is: The graph in Figure 3 is useful in estimating rDS values at any given value of VGS. The resistance is normalized to its specific value at VGS = 0 V. The dynamic range of rDS is shown as greater than 100:1, although for best control of rDS a range of 10:1 is normally used. V IN rDS V OUT + R ) r (1) DS It is assumed that the output voltage is not so large as to push the VCR out of the linear resistance region, and that the rDS is not shunted by the load. The lowest value which vOUT can assume is: 1000 VDS ¬ 0.1 V V IN rDS(on) V OUT(min) + R ) r DS(on) (2) rDS /r DS(on) ( W ) 100 r DS(on) r DS ] 1 – V GS V GS(off) 10 Signal Distortion: Causes Figure 2 shows that the bias lines bend down as VDS increases in a positive direction toward the pinch-off voltage of the FET. The bending of the bias lines results in a change in rDS, and hence the distortion encountered in VCR circuits; note that the distortion occurs in both the first and third quadrants. Distortion results because the channel depletion layer increases as VDS reduces the drain current so that a pinch-off condition is reached when VDS = VGS – VGS(off). Figure 5 shows how the current has an opposite effect in the third quadrant, increasing negatively with an increasingly negative VDS. This is due to the forward conduction of the gate-to-channel junction when the drain signal exceeds the negative gate bias voltage. Siliconix 10-Mar-97 1 0 0.2 0.4 0.6 0.8 1.0 VGS/VGS(off) Figure 3. Normalized rDS Data 2 AN105 +V 0 –V R Diode Cathode when Signal Swings Negative VOUT VCR VGS Reducing Signal Distortion The majority of VCR applications require that signal distortion be kept to a minimum. Also, numerous applications require large signal handling capability. A simple feedback technique may be used to reduce distortion while permitting large signal handling capability; a small amount of drain signal is coupled to the gate through a resistor divider network, as shown in Figure 6. The application of a part of the positive drain signal to the gate causes the channel depletion layer to decrease, with a corresponding increase in drain current. Increasing the drain current for a given drain voltage tends to linearize the VGS bias curves. On the negative half-cycle, a small negative voltage is coupled to the gate to reduce the amount of drain-gate forward bias. This in turn reduces the drain current and linearizes the bias lines. Now the channel resistance is dependent on the dc gate control voltage and not on the drain signal, unless the VDS = VGS – VGS(off) locus is approached. Resistors R2 and R3 in Figure 6 couple the drain signal to the gate; the resistor values are equal, so that symmetrical voltage-current characteristics are produced in both quadrants. The resistors must be sufficiently large to provide minimum loading to the circuit: VIN Diode Anode G – + Figure 5. Simple Attenuator Circuit R1 VCR Linearization R2 VIN – + R3 VCR VGG VOUT R2 = R3 // 10(rDS//Rload//R1) R2 = R3 w 10 [R1 ørDS (max) øRL] (3) Figure 6. Typically, 470-kW resistors will work well for most applications. R1 is selected so that the ratio of rDS(on) øRL to [(rDS(on) øRL) + R1] give the desired output voltage, or: rDS(on) ø R L (rDS(on) ø R L) ) R 1 R1 VO + VI R2 VIN R3 VCONTROL + VCR VOUT (4) Figure 7. The feedback technique used in Figure 6 requires that the gate control voltage, VGG, be twice as large as VGS in Figure 5 for the same rDS value. Use of a floating supply between the resistor junction and the FET gate will overcome this problem. The circuit is shown in Figure 7 and allows the gate control voltage to be the same value as that voltage used without a feedback circuit, while preserving the advantages to be gained through the feedback technique. 3 Siliconix 10-Mar-97 AN105 Experimental Results Figures 8 and 9 show low voltage output characteristic curves for a typical Siliconix n-channel voltage-controlled resistor, VCR7N. Bias conditions are shown both with and without feedback. Figure 8 shows a two-volt peak-to-peak signal on the VGS = 0 V bias curve, with the VCR operating in the first and third quadrants. The VCR is operated without feedback. The forward-biased gate-drain PN junction may be seen at approximately –0.6 V, and bending of the bias curve is apparent in the third quadrant. The photo also demonstrates the comparison between a fixed resistor (the linear line superimposed on the bias curve) and the distortion apparent in the VCR without feedback compensation; the VCR signal is unusable with the indicated amount of distortion at 2 V peak-to-peak. 200 VGS = VCONTROL VGS = VCONTROL = 0 V I D – Drain Current (mA) 100 I D – Drain Current (mA) VGS = 0 V 100 In Figure 9, the same VCR7N FET is shown operating with the addition of the feedback resistors. Distortion has been reduced to less than 0.5%, and the characteristics of the VCR are now closely comparable to those of a fixed resistor. In Figures 8 and 9, the same VCR FET characteristics are shown, with VGS adjusted for higher rDS. No feedback network is employed in Figure 8, and measured distortion is greater than 8%. In Figure 9, the feedback resistors have been added and distortion has been reduced to less than 0.5%. Some degree of non-linearity will be experienced in both the first and third quadrants as VGS approaches the FET cut-off voltage. For this reason, it is important that the feedback resistors be of equal value so that the non-linearities likewise will be equal in both quadrants. 200 0 VGS = –2.5 V 0 VGS = –3 V VCONTROL = –6 V –100 –100 –200 –1.0 –0.4 0 0.4 1.0 –200 –1.0 –0.4 0 0.4 1.0 VDS – Drain-Source Voltage (V) VDS – Drain-Source Voltage (V) Figure 8. VCR7N Without Feedback Figure 9. VCR7N With Feedback. Table 1: Distortion vs. Temperature Without Feedback Temperature Temperature (_C) +125 +25 –55 With Feedback rDS = rDS(on) 6% >5% 3.2% rDS = 10 rDS(on)