Controlled Resistor

• Vbe - gamma*Ic

voltage and a proportional voltage to the current going through it then the BJT will act like a common resistor(with in limits obviously).

possibly use a current multiplier to get gamma. By subtracting this voltage from Vc + Vbe we can get a fixed(independent of time) resistance.

floating(Rather than having to have it tied to one of the rails like DCR's).

uC, few resistors, and DAC's could do the job.

same thing more efficiently? There are not to many ways to achieve true floating voltage controlled resistors cheaply(in fact, I do not know any). Anyone have any ideas how it may be possible?

One way to make a programmable resistor is something like this:

We make a programmable resistor product that works a different way, in order to get bipolar/AC capability.

It really wasn't easy! And it's not cheap.

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Almost verbatim:

Except that you somehow have to put your voltage across Vc-Ve, but keep the current flowing through the extra Vbe to bias it.

It's easy to see this is just a "resistor follower", except instead of allowing hFE to set output impedance (for a straight RF, with a resistor from C to B, and sense connections from C to E, the impedance is Ro = R / hFE, give or take Vbe), instead a current mirror (almost) is used to set the base voltage, in which case hFE must be very large to load the resistor a minimal amount instead (the error is simply alpha = 1 - (1/hFE), so variation in hFE would still be the only concern).

There is no electronic way to vary the effective resistance, because by putting in a fixed resistor, and choosing algebra which runs around the transistor's characteristics, you've 1. done no better than the resistor itself, 2. you literally ARE using the resistor, just in a parallel current path, and 3. you cleanse the circuit from the wonderful characteristics that transistors offer.

The standard implementation of a voltage-variable amplifier (which can be used in a feedback loop to produce resistance) uses a diffamp with variable "tail" current. The input voltage, to first order, is simply the percentage between 0 and 100% from left to right. The actual relationship is hyperbolic, so this is only true for small differences (~20mV input, maybe

25-75% range in output current) before the distortion gets too bad (THD > 5% or so). Bipolar OTAs (operational transconductance amplifiers) use linearizing diodes on the input, which use the diode's exponential V-I characteristic to predistort a resistive input voltage, extending it to 90 or 95% at reasonable linearity. More range is possible, usually with lots of tweaking.

Unlike in SPICE, multiplier blocks aren't cheap -- AD633 is a fairly old multiplier, quite accurate, four quadrant operation, still available and well stocked. It's still $10 a pop in single quantities. Multiplying ADCs (essentially digitally selectable resistor dividers) are noticably cheaper, and probably have the same or better bandwidth between REF and OUT (>1MHz).

The standard analog method to create a voltage-variable resistor (one quadrant) is a JFET with feedback resistors. The feedback tends to linearize the V-I characteristic (extending the natural 'resistive' range), while the quadratic transfer function keeps things nonlinear enough to perform multiplication.

Tim

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"James Brown"  wrote in message 
news:2099139.4716.1331514268403.JavaMail.geo-discussion-forums@ynne2...
A BJT has an effective resistance of

R = (Vc - Ve)/Ic

but since Ve = Vb - Vbe

R = (Vc + Vbe - Vb)/Ic

For it to act like a true resistor(that is, R' ~= 0) then if we can set Vb = 
Vc + Vbe - gamma*Ic

We have

R = gamma

That is, If we program the base of a BJT with with the sum of a constant 
voltage and a proportional voltage to the current going through it then the 
BJT will act like a common resistor(with in limits obviously).


Is this possible to achieve? We can get Ic through a current mirror and 
possibly use a current multiplier to get gamma. By subtracting this voltage 
from Vc + Vbe we can get a fixed(independent of time) resistance.

This could lead to a voltage or current controlled resistance and possibly 
floating(Rather than having to have it tied to one of the rails like DCR's).

It would be quite easy to program the base of a BJT to achieve such results. 
A uC, few resistors, and DAC's could do the job.

The question is, can anyone come up with a suitable discrete topology to do 
the same thing more efficiently? There are not to many ways to achieve true 
floating voltage controlled resistors cheaply(in fact, I do not know any). 
Anyone have any ideas how it may be possible?

Vc + Vbe - gamma*Ic

voltage and a proportional voltage to the current going through it then the BJT will act like a common resistor(with in limits obviously).

possibly use a current multiplier to get gamma. By subtracting this voltage from Vc + Vbe we can get a fixed(independent of time) resistance.

floating(Rather than having to have it tied to one of the rails like DCR's).

uC, few resistors, and DAC's could do the job.

the same thing more efficiently? There are not to many ways to achieve true floating voltage controlled resistors cheaply(in fact, I do not know any). Anyone have any ideas how it may be possible?

What do you plan on doing with the bias voltage or source of where it comes from? Is that going to rain on your parade as it becomes part of the circuit you are using your BJT in as a R ?

Jamie

voltage and a proportional voltage to the current going through it then the BJT will act like a common resistor

The slick way to do up the programmable transconductance of a transistor, is the old OTA (operational transconductance amplifier) circuit. The result is a current-programmed three terminal device, with delta-V on two terminals times the program current times a constant equalling an output current (on the third terminal) See LM13700 datasheet for more information, or look up the large number of app notes on the old CA3080 from RCA/Harris/Intersil.

This makes a three-terminal resistor, with only ONE current-carrying terminal, and two voltage-sensing terminals; it only is a good 'resistor' linear component for program currents in the 1 uA to 1 mA range, output current in the +/- 1 mA range, and input voltages of +/- a few dozen millivolts.

Three other ways to make voltage-variable resistance are JFET (but only with the source grounded, and only for low voltages), or with a photoresistor (programmed with a lightsource), or using an analog multiplier.

The photoresistor or JFET are not completely linear in the control-input voltage. The JFET or the multiplier will have only one available current-carrying terminal, just like the OTA. The analog multiplier is likely to be expensive.

So, most people who want an adjustable resistance end up with some kind of digital potentiometer (basically just a DAC based on switched resistances).