### AN102-JFET Biasing Techniques

```AN102
JFET Biasing Techniques
Introduction
Engineers who are not familiar with proper biasing methods
often design FET amplifiers that are unnecessarily sensitive
to device characteristics.
One way to obtain consistent circuit performance, in spite
of device variations, is to use a combination of constant
voltage and self biasing. The combined circuit configuration
turns out to be the same as that generally used with bipolar
transistors, but its operation and design are quite different.
input signal variations of 0.2 V will produce output
voltage swings of 7.0 V, and a voltage gain of 35 where:
g fs R D
AV 1 R g
D os
(1)
g os JFET output conductance
In most applications, RD gos is negligible, therefore:
(2)
Constant-Voltage Bias
Three Basic Circuits
Let’s examine three basic common-source circuits that can
be used to establish a FET’s operating point (Q-point) and
then see how two of them can be combined to provide
greatly improved performance.
The three basic biasing schemes are:
Constant-voltage bias, which is most useful for RF and
video amplifiers employing small dc drain resistors.
Constant-current bias, which is best suited to low-drift
dc amplifier applications such as source followers and
source-coupled differential pairs.
Self bias (also called source bias or automatic bias),
which is a somewhat universal scheme particularly
valuable for ac amplifiers.
The Q-point established by the intersection of the load line
and the VGS = –0.4 V output characteristic of Figure 1
provides a convenient starting point for the circuit
comparison. The load line shows that a drain supply voltage,
VDD, of 30 V and a drain resistance, RD, of 39 k are being
used.
The quiescent drain-to-source voltage, VDSQ, is 16 V,
allowing large signal excursions at the drain. Maximum
The constant-voltage bias circuit (Figure 2) is analyzed
by superimposing a line for VGG = constant on the transfer
characteristic of the FET (2N4339 typical device).
The transfer characteristic is a plot of ID vs. VGS for
constant VDS. Since the curve doesn’t change much with
changes in VDS, it is useful in establishing operating bias
points. In fact, it is probably more useful than the output
characteristics because its curvature clearly warns of the
distortion to be expected with large input signals.
Furthermore, when a bias load line is superimposed,
allowable signal excursions become evident, and input
voltage, gate-source signal voltage, and output signal
current calculations may be made graphically.
The heavy vertical line at VGS = –0.4 V establishes the
Q-point of Figure 1. No voltage is dropped across resistor
RG because the gate current is essentially zero. RG serves
mainly to isolate the input signal from the VGG supply.
Excursions of the input signal, eg, combine in series with
VGS so that they add algebraically to the fixed value of
–0.4 V. The effect of signal variation is to instantaneously
shift the bias line horizontally without changing its slope.
The shifting bias line then develops the output signal
current (Figure 2).
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Siliconix
10-Mar-97
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1.5
+VDD
VDS = 15 V
1.2
RD
VGS = 0
1.2
–0.2 V
0.9
I D (mA)
I D (mA)
0.9
RD = 39 k
0.6
–0.4 V
Output
eg
Constant
VGG Load
Line
RG
–VGG
0.6
ID
–0.6 V
0.3
0.3
–0.8 V
0
VGS(off)
0
0
10
20
30
40
50
0
–0.8
VDS (V)
1.5
RD
1.5
eg
RG
0.9
Output
ID
ac Load Line
0.6
VDS = 15 V
1.2
I D (mA)
I D (mA)
1.2
Figure 2. Transfer Curve—Constant-voltage bias is
maintained by the VGG supply as shown on this
typical transfer curve. Input signal eg moves the
load line horizontally.
+VDD
VDS = 15 V
0.9
ac Load Line
Slope – wC
0.6
ID
Signal
0.3
–1.6
VGS (V)
eg
Figure 1. Output Characteristic Curve—A large dynamic
range is provided by the operating point at
VDSQ = 15 V, IDQ= 0.4 mA, and VGSQ = –0.4 V.
–1.2
0.3
dc Load Line
0
dc Load Line
0
0
–0.4
eg = 0.1 V pk Signal
–0.8
–1.2
–1.6
VGS (V)
0
–0.4
eg
–0.8
–1.2
–1.6
VGS (V)
Figure 3. Constant-current bias fixes the output voltage for
any RD. Hence, input signals cannot affect the
output unless the current source is bypassed.
Figure 4. Partial bypassing of the current source (Figure 3)
Lowers the circuit gain by tilting the ac load line
from the vertical. The capacitor drop subtracts
from eg.
Constant-Current Bias
horizontally and produce no gate-source voltage
excursion. This bias technique is therefore limited to
source followers, source coupled differential amplifiers,
and ac amplifiers where the source terminal is bypassed
to ground at the signal frequency.
The constant-current bias approach (Figure 3) for
establishing the Q-point of Figure 1 requires a 0.4-mA
current source. For an ideal constant-current generator,
input signal excursions merely shift the bias line
2
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If an ac ground is provided by a bypass capacitor across
the current source, a vertical ac bias line will be
established. Input signal variations will then translate the
ac bias line horizontally, and signal development will
proceed as with constant-voltage biasing (Figure 3).
This will lower the gain of the amplifier because of signal
degeneration at the source. The input signal, eg, is
reduced by the drop across the capacitor:
VGS = eg – VS = eg – iSXC
(3)
It is clear from Figure 4 that the input signal shifts the
operating point only by an amount equal to VGS, the
effective input signal. As the signal frequency is
decreased, the slope of the ac bias line decreases, causing
the effective input signal to approach zero.
Self-Bias Needs No Extra Supply
The self-bias circuit (Figure 5) establishes the Q-point by
applying the voltage dropped across the source resistor,
RS, to the gate. Since no voltage is dropped across RS
when ID = 0, the self-bias load line passes through the
origin. Its slope is given by –1/RS = IDQ/VGSQ.
Signal development is the same as in the case of the
partially bypassed constant-current scheme except that
the load line is a dc bias line. Signal degeneration is
described by Equation 1 with XC replaced by RS. The ac
gain of the circuit can be increased by shunting RS with
a bypass capacitor, as in the constant-current case. The ac
load line then passes through the Q-point with a slope
–(1/ZS) = – (wC + 1/RS).
Siliconix
10-Mar-97
VDS = 15 V
+VDD
RD
1.2
I D (mA)
Should the bypass capacitor not provide a sufficiently low
reactance at the signal frequency, the ac bias line will not be
be vertical. It will still intersect the transfer curve at the
Q-point but with a slope equal to –(1/XC) = –wC (Figure 4).
1.5
Output
eg
RG
0.9
RS
Self-Bias dc
Load Line
0.6
ID
0.3
0
0
eg
–0.4
–0.8
–1.2
–1.6
VGS (V)
Figure 5. The self-bias load line passes through the origin
with a slope –1/RS. Bypassing RS will steepen
the slope and increase the gain of the circuit.
The circuit is biased automatically at the desired Q-point,
requiring no extra power supply, and providing a degree
of current stabilization not possible with constant-voltage
biasing.
Combo Constant-Current/Self-Biasing
A fourth biasing method, combining the advantages of
constant-current biasing and self biasing, is obtained by
combining the constant-voltage circuit with the self-bias
circuit (Figure 6). A principal advantage of this
configuration is that an approximation may be made to
constant-current bias without any additional power supply.
The bias load line may be drawn through the selected
Q-point and given any desired slope by properly choosing
VGG. (The bias line intercepts the VGS axis at VGG.) The
larger VGG is made, the larger RS will be and the better will
be the approximation to constant-current biasing.
All three circuits in Figure 6 are equivalent. Circuit 6a
requires an extra power supply. The need for an additional
supply is avoided in 6b by deriving VGG from the drain
supply. R1 and R2 are simply a voltage divider. To
maintain the high input impedance of the FET, R1 and R2
must both be very large.
Very large resistors cannot always be found in the exact
ratio needed to derive the desired VGG in every circuit
application. Circuit 6c overcomes this problem by
placing a large RG between the center point of the divider
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and the gate. This allows R1 and R2 to be small, without
lowering the input impedance.
One point of caution is that as VGG is increased, VS
increases, and VDS decreases. Therefore, with low VDD,
there may be a significant decrease in the allowable
output voltage swing.
Biasing for Device Variations
The value of the combination-bias technique becomes
apparent when one considers the normal production
spread of device characteristics. The problem is
illustrated in Figure 7 where the lower and higher ranges
of the 2N4339 devices are shown. The two curves
illustrate the operating current variations using various
types of biasing in a normal production lot. Other devices
with even wider min/max IDSS limits will show wider
variations.
Attempting to establish suitable constant-voltage bias
conditions for a production spread of devices is practical
only for circuits with very small values of dc drain resistance
—for example, circuits with inductive loads. As the
constant-voltage bias plot of Figure 7a reveals, constant gate
bias causes a significant difference in operating IDQ for the
extreme limit devices. At VGS = –0.4 V, the range of IDQ
is 0.13 to 0.69 mA, and VGSQ for a given RD will vary
greatly for most resistance-loaded circuits. For the example
of Figure 1, with RD = 39 kW and VDD = 30 V, VGSO varies
from near saturation (5 V) to 25 V.
An excellent method of biasing is the
constantĆcurrent method of Figure 3. Biasing in this
manner fixes the operating drain current for all
devices and sets VDSQ to VDD - IDQRL for any
device in the production spread. VGS automatically
finds a value to set the appropriate IDQ = constant
for all devices. For the constantĆcurrent bias plot of
Figure 7b, with IDQ = 0.4 mA, VGS would range
from -0.11 to -0.67 V.
Output characteristics are not needed as long as IDQ is
chosen to be below the minimum IDSS. With RD = 39 kW
and VDD = 30 V, VDSQ is 14.8 V for all devices.
The disadvantages of the constantĆcurrent method are
that it allows no signal to be developed unless the current
source is bypassed and, as we shall see, it lacks the
4
flexibility to provide constant gain despite variations in
the forward transconductance, gfs, of the devices.
The selfĆbias scheme is a reasonable choice for
singleĆended dc amplifiers and for ac amplifiers. In
unbypassed or dc circuits, some compromise must be
made between the gain loss due to current feedback
degeneration and the advantage of current stabilization
achieved with high RS.
An appropriate choice of IDQ limits can be made by
using the pair of limiting transfer curves. For example,
for RS = 1 kW, the load line shown on the selfĆbias
curve of Figure 7c is established. The maximum I D
is 0.52 mA, and the minimum ID is 0.24 mA. The
operating range of VDSQ may be calculated for any
value of VDD and RD . Clearly, for RD = 39 kW, the
maximumĆlimit device (device B) would operate
with VDSQ = 9.8 V and the minimumĆlimit device
(device A) would operate with V DSQ = 20.6 V. This
results in satisfactory operation for all devices.
However, such a variation in I DQ imposes severe
limitations on the circuit design.
A better approach is illustrated by the combinationĆbias
curve of Figure 7d with VGG = 1.2 V. The range of IDQ
for the bias condition is 0.25 mA to 0.32 mA.
A similar minimum difference in IDQ could be achieved
with RS = 6 kW and VGG = 0 (a selfĆbias condition) but
the operating points would be pushed toward the toe of
the transfer characteristics and allowable signal input
would be reduced.
The combination circuit (Figure 7d) allows almost ideal
operation over the full production spread of devices.
Even with RD = 6 kWā, the VDSQ would range only
between 10 and 15 V.
For the combination circuit, RD should be chosen to
allow the largest output signal swing for IDQ midway
between the two extremes of 0.25 and 0.32 mA; namely
0.285 mA. Setting the voltage drop across RD at oneĆhalf
of (VDD - 2 VGS(off)typ) or 14 V, (30Ć2)1/2 yields RD =
(14 V/0.285 mA) = 49 kW.
Figure 10 shows the effect of temperature variation on
the transfer characteristics from 25 to 125_C. The
opposite change occurs from 25 to -55_C. The
temperature effect is generally far less than the
deviceĆtoĆdevice variation.
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10-Mar-97
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+VDD
+VDD
(a)
+VDD
(b)
(c)
RD
R2
Output
Output
eg
RD
RG
eg
RG
R2
RD
Output
eg
RS
R1
R1
RS
RS
+VGG
1.5
VDS = 15 V
I D (mA)
1.2
1.6
VGG
1.2
0.8
0.9
0.6
0.4
RS = 5 k
0
–0.4
–0.8
VGS (V)
–1.2
–1.6
Figure 6. All three combination-bias circuits are equivalent. They add constant-voltage biasing to the self-bias circuit to
extablish a reasonably flat load line without sacrificing dynamic range.
1.5
(a)
1.5
(b)
VDS = 15 V
VDS = 15 V
1.2
I D (mA)
I D (mA)
1.2
0.9
QB
0.6
0.9
0.6
QA
0.3
0.3
QA
0
0
0
–0.4
–0.8
VGG = –0.4 V V (V)
GS
(c)
–1.2
–1.6
0
1.5
(d)
–0.4
–0.8
–1.2
VGS (V)
–1.6
1.5
VDS = 15 V
VDS = 15 V
1.2
1.2
0.9
I D (mA)
I D (mA)
QB
RS = 1 k
0.6
QB
0.3
0.9
0.6
RS = 6 kW
0.3
QA
QB
QA
0
0
–0.4
–0.8
VGS (V)
–1.2
–1.6
1.6
1.2
0.8
0.4
0
–0.4
–0.8
–1.2
–1.6
VGS (V)
Figure 7. Transfer Characterisitc Curves—2N4339: The advantages of combination biasing, when one is working with a spread
of device characteristics, are made obvious by plotting the load lines for the various types of biasing on a pair of
limiting transfer curves.
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10-Mar-97
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Minimize The Gain Variations
Leaving RS unbypassed helps reduce gain variations
from device to device by providing degenerative current
feedback. However, this method for minimizing gain
variations is only effective when a substantial amount of
gain is sacrificed.
A better approach is to use the combinationĆbias
technique with the bias point selected from the transfer
and transconductance curves (Figure 8).
values. Thus, a constant, or nearly constant, stage gain is
obtained even with a bypass capacitor.
The design procedure is as follows:
Step 1.
Select a desired IDQA below IDSSA. A good value,
allowing for temperature variations, is 60% of
IDSSA. This will allow for decreasing IDSS due to
temperature variation and for reasonable signal
excursions in load current.
Step 2.
Enter the transfer curves at IDQA 0.6 IDSSA
(0.3 mA) to find VGSQA. Thus VGSQA –0.2.
Step 3.
Drop vertically at VGSQA to the minimum limit
transconductance curve to find gfsQA. The value as
read from the plot is approximately 1000 mS.
Step 4.
Travel across the gfs plot to the maximum
curve to find VGSQB at the same value of gfs.
This is VGSQB –0.7 V.
Step 5.
Travel vertically up to the maximum limit
transfer curve to find IDQB at VGSQB. This is
IDQB 0.36 mA.
Step 6.
Construct an RS bias line through points QA and
QB on the transfer curves. The slope of the line is
1/RS, and the intercept with the VGS axis is the
required VGG.
1.5
VDS = 15 V
I D (mA)
1.2
0.9
0.6
QA
QB
0
0
–0.4
–0.8
–1.2
–1.6
VGS (V)
As Figure 8 demonstrates, it may be somewhat
inconvenient to perform Step 6 graphically. An algebraic
solution can be employed instead. The source resistance
is given by
2000
g fs (mS)
1600
1200
RS = (VGSQA – VGSQB) / (IDQB – IDQA)
QA
QB
(4)
and the bias voltage is
800
VGG = RSIDQB + VGSQB
(5)
400
0
0
–0.4
–0.8
–1.2
VGS (V)
–1.6
Figure 8. Gain variations are minimized when the load line
is designed to intersect the pair of limiting
transfer curves (top) at points of equal
gfs (bottom).
As Figure 8 shows, it is possible to find an RS and a VGG
that will set IDQA and IDQB to values such that gfsQ will
be the same for both devices. The gfsQ of all intermediate
devices will be approximately equal to the limiting
6
Care should be taken to maintain the proper algebraic
signs in Equations 4 and 5. For n-channel FETs, VGS is
negative and ID is positive. For p-channel units, the signs
are reversed.
If the transconductance curves of Figure 8 are not
available, gfs can be determined simply by measuring the
slope of the transfer curve at the desired operating point.
Just place a straight-edge tangent to the curve at the
Q-point and note the points at which it intercepts the ID
and VGS axes. The slope and gfs are given by:
slope = gfs = ID(intercept) / – VGS(intercept)
(6)
In designing a constant-gain circuit, simply set the
straight-edge tangent to the transfer curve of device A at
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10-Mar-97
AN102
point QA and slide it, without changing its slope, until it is
tangent to the curve of device B. The tangent point is QB.
Before getting into the details of bias-circuit design,
several general observations can be made about the
circuits of Figure 9:
FET Source-Follower Circuits
Circuits a, c, e and g can accept only positive and
small negative signals, because these circuits have
their source resistors connected to ground. The other
circuits can handle large positive and negative signals
limited only by the available supply voltages and device breakdown voltage.
Circuits c, d, g and h employ current sources to improve drain-current (ID) stability and increase gain.
Circuits d and h employ JFETs as current sources.
Circuits d, f and h employ a source resistor, RS, which
may be selected to set the quiescent output voltage
equal to zero.
Circuits d and h use matched FETs. RS is selected to
set ID . The dc input-output offset voltage is zero.
The common-drain amplifier, or source follower, is a
particularly valuable configuration; its high input
impedance and low output impedance make it very useful
for impedance transformations between FETs and bipolar
transistors. By considering eight circuits (Figure 9),
which represent virtually every source-follower
configuration, the designer can obtain consistent circuit
performance despite wide device variations.
There are two basic connections for source followers:
with and without gate feedback. Each connection comes
in several variations. Circuits 9a through 9d have no gate
feedback; their input impedances, therefore, are equal to
RG. Circuits 9e through 9h employ feedback to their gates
to increase the input impedance above RG.
VDD
VDD
VDD
VDD
A
RG
RS
RG
RS
RG
IS
Q1
RG
R S1
B
C
Q2
R S2
D
–VSS
(a)
(b)
–VSS
(c)
VDD
VDD
(d)
VDD
VDD
Q1
RG
RS
RG
RS
RG
RS
RG
R S1
Q2
R1
R1
R S2
IS
–VSS
(e)
(f)
–VSS
(g)
(h)
Figure 9. Virtually every practical source-follower configuration is represented in this collection of eight circuits. The
configurations in the top row do not employ gate feedback; the corresponding configurations in the bottom row
employ gate feedback.
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10-Mar-97
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1.5
1.5
VDS = 15 V
VDS = 15 V
2N4339
ID (mA)
1.2
ID (mA)
TA = 25_C
0.9
RS = 1 k
125_C
25_C
0.6
1.2
0.9
0.6
RS = 50 k , VSS = –15 V
0.3
125_C
RS = 10 k , VSS = –1.6 V
0
0
–0.4
–0.8
VGS (V)
–1.2
–1.6
1.2
Figure 10. Self-biasing (Figure 9a) uses the voltage
dropped across the source resistor, RS to bias
the gate. The load line passes through the
origin and has a slope of –1/RS.
0.8
0.4
0
VGS (V)
–0.8
–1.2
–1.6
Figure 11. Adding a VSS Supply to the self-bias circuit
(Figure 9b) allows it to handle large negative
signals. The load line’s intercept with the VGS
axis is at VGS = VSS. Bias Lines are shown for
VSS = –15 V and VSS = –1.6 V.
1.5
1.5
VDS = 15 V
VDS = 15 V
1.2
I D (mA)
1.2
ID (mA)
–0.4
0.9
RS = 1 k
0.8
RS2 = 1.5 k
0.6
RS + R1 = 10 k
0.4
RS + R1 = 10 k
0.3
0
0
–0.4
–0.8
VGS (V)
–1.2
–1.6
Figure 12. This load line is set by RS2 and Q2 which acts as a
current source (Figure 9d). This source follower,
therefore, exhibits zero or near-zero offset. If the FETs
are matched at the operating ID, the source follower
will exhibit zero or near-zero temperature drift.
Biasing Without Feedback Is Simple
Circuit 9b is an example of source-resistor biasing with
a –VSS supply added. The advantage over circuit 9a is
that the signal voltage can swing negative to
approximately –V SS . Two bias lines are shown in
Figure 11, one for V SS = –15 V and the other V SS =
–1.6 V. For the first case, the quiescent output voltage
lies between 0.18 and 0.74 V. For the second, it lies
between 0.3 and 0.82 V.
8
0.8
0.4
0
–0.4
–0.8
VGS (V)
–1.2
–1.6
Figure 13. The bias load line is set by RS but the output load
line is determined by RS + R1 when gate feedback
is employed (Figure 9e). The feedback VFB is
determined by the intercept of the RS + R1 load
line and the VGS axis.
A pair of matched FETs is used in the circuit of Figure 9d,
one as a source follower and the other as a current source.
The operating drain current (IDQ) is set by RS2, as
indicated by the load line of Figure 13. In this illustration
the drain current may be anywhere from 0.2 to 0.42 mA,
as shown by the limiting transfer characteristic intercepts;
however, VGS1 = VGS2 because the FETs are matched.
Other dual devices, such as 2N5912 and SST441, can
operate at 5 mA and frequencies above 400 MHz.
Siliconix
10-Mar-97
AN102
feedback. The bias load line is set by RS (Figure 13). The
output load line, however is determined by the sum of RS
+ R1. The feedback voltage VFB, measured at the junction
of RS and R1, is determined by the intercept of the RS +
R1 load line with the VGS axis. The quiescent output
voltage is VFB – VGS.
1.5
VDS = 15 V
I D (mA)
1.2
0.8
RS = 670 W
RS + R1 = 50 kW
VSS = –15 V
0.4
In the circuit of Figure 9f, RS can be trimmed to provide
zero offset. As the curves show (Figure 14), RS will be
between 670 W and 2.5 kW. RS is much less than R1. The
source load line intercepts the VGS axis at VSS = –VGG =
–15 V.
RS = 2.5 kW
VGS (V)
Figure 14. RS can be trimmed to provide zero offset at
some point between 670 w and 2.5 kW
(Figure 9f). The source load line intercepts
the VGS axis at VSS = VGG = –15 V. Note
that this load line is not perfectly flat. it has a
slope of –1/50 kw , because the current source
is not perfect; it has a finite impedance.
Practical Amplifier Biasing Examples
All commercially available JFET part numbers exhibit a
significant variation in the IDSS and VGS(off) parameters.
Applying the Figure 9a and 9d biasing configurations,
Figures 15 and 16 provide typical worst case
drain-current extremes as a function of source resistance.
Plotted are the popular low-current amplifiers.
Biasing With Feedback Increases ZIN
Each of the feedback-type source followers (Figure 9e
through 9h) is biased by a method similar to that used with
the nonfeedback circuit above it. However, in each case,
RG is returned to a point in the source circuit that provides
almost unity feedback to the lower end of RG. If RS is
chosen so that RG is returned to zero dc volts (except in
circuit 9e), then the input/output offset is zero. R1 is
usually much larger than RS.
Circuit 9e is useful principally for ac-coupled circuits. RS
is usually much less than R1 to provide near-unity
Part Number
Package
2N4338, 2N4339
TO-206AA (TO-18) Metal Can
J201, J202, 2N5484
TO-226AA (TO-92)
Through-Hole Plastic
SST201, SST202, SST5484
TO-236 (SOT-23) Surface Mount
Applying the Figure 9a biasing technique to a
small-signal amplifier circuit as illustrated in Figure 17,
results in typical voltage gain as plotted in Figure 18.
Note that as the drain current decreases the overall gain
increases since RD can be greater, despite
transconductance gfs decreasing.
2
2
I D – Drain Current (mA)
2N4339 Max.
0.5
SST/J201 Min.
VDD = 4 to 20 V
0.1
0.05
RG
RS
SST/J202 Max.
1
I D – Drain Current (mA)
SST/J201 Max.
1
SST5484
2N5484 Max.
SST5484
2N5484 Min.
0.5
2N4338 Min.
0.1
VDD = 4 to 20 V
0.05
RG
0.01
RS
2N4338 Max
SST/J202 Min.
2N4339 Min.
0.01
0.1
0.5
1
RS – Source Resistance (kW)
5
Figure 15. JFET Source Biased Drain-Current
vs. Source Resistance
Siliconix
10-Mar-97
10
0.1
0.5
1
RS – Source Resistance (kW)
5
10
Figure 16. JFET Source Biased Drain-Current
vs. Source Resistance
9
AN102
200
VDD
160
VO
VIN
RS
CS
A V – Voltage Gain
RD
RG
g fs R D
AV 1 R g
D os
Assume VDD = 15 V, VDS = 5 V
10 V
RD I
D
120
2N4338/9
SST/J201
80
SST/2N5485
40
SST/J202
0
0.01
0.1
1
ID – Drain Current (mA)
Figure 17. JFET Source Biased Amplifier
10
Figure 18. Circuit Voltage Gain vs. Drain-Current
Siliconix
10-Mar-97
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