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From: Winfield Hill
Subject: Re: Voltage Controlled Resistor?
Date: 12 Dec 2002 19:13:25 -0800
Organization: Rowland Institute
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Tony Williams wrote...
> Winfield Hill wrote:
>> IN o--+-----------------,
>> | ______ |
>> | | | |
>> R1 | Q1 | | Q2
>> | | |/ \| Vc
>> +----+----| |---o
>> | |\V V/|
>> | __ |_____| matched NPN
>> '---|- \ | transistors
>> | \______|
>> | /
>> The current in R1 and hence Q1 is I1 = Vin/R1, so Vbe1 from
>> Eber-Molls is Vbe1 = VT ln(I1/Is), where VT = kT/q and Is is
>> the reverse saturation current (which in a complete setup
>> would ultimately disappear from our equations). Seeing that
>> Vbe2 = Vc + Vbe1, we can determine I2 as a function of Vc,
>> I2 = Is e^ (Vc/Vt + ln(I1/Is)). This can be manipulated into
>> an I2 = I1 * K form, where K is an exponential function of Vc.
>> So we see Rin = R1 in parallel with a programmable resistance.
>> Isolating R1's current from the IN terminal with a follower,
>> and deriving Vc from a current into a logging transistor to
>> fix the exponential-function issue, can clean up the control
> I'd already got as far as ln(I2/I1) = Vc*(q/kT) and
> therefore the actual incoming control voltage would
> have to be logged, such that Vc = kT/q * ln(Vin).
> This would give I2 = I1 * Vin.
> Rout = Vout/Iout = Vout/(I1+I2) = Vout/I1(1 + Vin).
> And the easiest way to get rid of the non-linearity
> due to the (1 + Vin) term is to buffer R1, so that
> Iout does not have to include the I1 current to R1.
>> Two more transistors and three more opamps later ...
OK, i'll indulge myself. Here's the full drawing and formula
for R ~ control voltage. R_in = R1 (Vset/Vref)(R3/R2), if
I avoided mixing up a numerator and denominator someplace!
. Rin = 1.0k Vset/10
. IN o----------------, ___ R3 ___ Vref = 10V
. G =_+1 | | 10k
. __ R1 ___/ |___| __ | ___ R2___ Vset
. | 2.0k \_| | __/ -|----+ | 20k 0 to +10V
. |_________ | | \_+|--G | |_________
. | | | | | | |
. | Q1 |/ Q2 \| | |/ Q3 \| Q4 |
. +-------| |---+--------| |-------+
. | |\V V/| |\V V/| |
. | __ |_____| matched NPN |_____| __ |
. '--|- \______| transistors |______/- |--'
. G --|+_/ \+_|-- G
If Q1-Q2 and Q3-Q4 are each matched to 25uV, and with a beta
approaching 1000, the formula should be accurate to about 0.1%
Alternately a few trim-point adjustments can be added.
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