Using an OTA to Simulate a Floating Resistor: Generating Small Currents

[avih7531]

Hi all,

I came across this paper which details using OTAs to simulate a floating resistor: https://drive.google.com/file/d/1AnAYBmrt577W5yd3mFiRc6gZMQo8c083/view

Fg. 3 demonstrates the circuit for a floating resistor:


The formula (as mentioned right after Fg. 1) is R=(2V_t)/I_b where V_t = 26mv (at room temp) and I_b is the current through the base.

Easy enough...right?

Section 3 of the paper says that the theoretical resistance values measured between 52Ω and 520kΩ using an I_b values between 0.1uA to 1mA. Solid range of values!

I would very much like to incorporate this into an "analog circuit, digital brain" guitar pedal, although I cannot fathom how to create stable currents from an Arduino or the like.

I really would like to avoid digipots and vactrols, so if this method is possible to fit in a guitar pedal, I'd love to incorporate it!

Any ideas on how to generate stable currents that small would be greatly appreciated!

[avih7531]

Could a current divider work here, maybe?

[T3sl4co1l]

Set up a timer PWM channel, run it into an RC filter (the higher order and lower cutoff, the better, to reduce ripple at the output; but also not so slow that the response rate is obnoxious), then a resistor into the bias pin(s).  Note that the bias pin has a low impedance (it's approximately a diode drop to -V), you can't just wire an RC lowpass to it, the low impedance effectively shorts out the capacitance so you need exponentially more for the same effect.  Instead you need to filter the voltage, then convert voltage to current with a series resistor.

The faster the timer runs, the better; probably it'll be 1x prescaler, 16 bit timer, and if clock is say 16MHz or more, a count of some thousands still gets you a PWM frequency in the kHz which should be quite easy to filter while keeping a human-scale response time (i.e. under 100ms say).

Note that ripple here causes signal modulation (AM, or frequency response too if you're using this artificial resistor in a filter).  Which kind of oddly distorts the signal plus making it buzz with the PWM tone.  But since you're after effects, maybe that's valuable, say by mixing another signal into the filtered PWM offset.  Which could be the signal itself (getting some squaring action, enhancing even-order distortion), another signal, or just other synth signals (say, varying the PWM with a slow sine or triangle wave to get a tremelo effect).

Also note it only works over the voltage range the amp is rated for, so, LM13700 only pulls up/down to within a volt or two of the supplies.  A 5V supply isn't really enough to work with, but +/-5V would be okay, or +/- 9V or more.  Your digital control will need some analog level shifting, because it can't pull down to -9V or whatever.  Probably a cascode is the easiest way to do this: use a PNP, base to GND, emitter to voltage-to-current-converting series resistor to PWM filter, collector to bias pin(s).

I think it also only works for small signals, in the range where the inputs are reasonably (trans)linear; so, 10s of mV.  It's not something you can wire up just like any random resistor.  For larger signals, the current will simply saturate (max out to +/- Iabc, or more if you're using the Darlington follower sections).

Tim

[Terry Bites]

Generate Ib from a resistor as shown in fig 28 https://www.ti.com/lit/gpn/lm13700

See figs 35-37 https://www.edn.com/a-guide-to-using-fets-for-voltage-controlled-circuits-part-4/
for some less tricky VCBPFs

[T3sl4co1l]

Two op-amps and MOSFETs just to bleed a few microamperes somewhere? I know TI is bad these days but man...

Tim

[Terry Bites]

Well, start with precsion and work your way down...
A 15k resistor will do , you're right.