## NG-SPICE: Biasing the Default Transistor for Ideal Linear Voltage Gain, at 3V.

In recent days and weeks, I’ve been studying some of my own ideas, concerning the creative uses of the N-Channel, Enhancement-Mode, MOSFET. And to help me explore that subject, I’ve used An Open-Source Circuit Simulation Program called ‘NG-SPICE’. One big problem with this approach is the fact that the default transistor that the software assumes the power-user wants to use, is clearly not meant for Linear Voltage Amplification in the 100kHz-1.0Mhz frequency range, and with a 3V supply voltage. This transistor type is meant to be operated at higher voltages, and mainly, for digital uses. All the software is geared for Integrated Circuit Emphasis. But, I have looked at possible ways in which the default transistor could still be used under the conditions I’m more interested in. In theory, I could change the parameters of the transistor involved as much as I like, until I’ve made a high-speed, low-voltage transistor out of it. One problem with that is the fact that I give the software the geometry of the transistor on a chip, and the software then derives many of its assumed properties. I don’t know much about IC design, so I probably would not obtain the kind of transistor I’m looking for, if I tried to invent one.

So the question comes back, what is the best way to bias this one, arbitrary transistor-type, to act as a high-impedance amplifier under the conditions written above? And how much gain does it give me? The answer seems to be, that when connected as below, the best performance I can obtain is an Alpha of (-5.25): What I’ve also learned is, that the bias voltage associated with this circuit, with respect to ground, is (+2.14V). With respect to the supply voltage, that is (-0.86V). 3.75μV of bias current would need to flow. This information would be useful if an attempt ever came along to implement This Idea.

(Edit 7/5/2019, 17h15 : )

Doubling (VGS – VT0) of M1 would have as effect, that IDS quadruples. It would also have as effect, that equal, small changes in Gate Voltage translate into doubled changes in IDS. But, if the increase in bias current was taken into account by the circuit designer, by putting a resistor of merely 100kΩ in series with M1, thereby achieving that the supply voltage was ideally halved again as a result, then this would finally have as effect to halve the net voltage gain at the Drain of M1.

It would also have as effect, to quarter output impedance, which would be desirable from the last of a series of these stages, ending in a realistic load of some kind.

(End of Edit, 7/5/2019, 17h15.)

The Model-Card of the transistor is linked below:

http://dirkmittler.homeip.net/text/NMOS1.mod.txt

To pursue the exact subject of the earlier posting, about Variable-Gain Amplifiers, I also felt that it would be necessary to add to the circuit the components, that would transform it into a variable attenuator. And the following schematic shows how I did that:

(Updated 7/16/2019, 7h50 … )

## Thoughts About Software Equalizers

If a software-equalizer possesses GUI controls that correspond to approximate octaves, or repeated 1-2-5 sequences, it is entirely likely to be implemented as a set of bandpass filters acting in parallel. However, the simplistic bandpass filters I was contemplating, would also have required that the signal be multiplied by a factor of 4, to achieve unit gain where their low-pass and high-pass cutoff frequencies join, as I described in this posting.

(Edit 03/23/2017:

Actually, the parameters which define each digital filter, are non-trivial to compute, but nevertheless computable when the translation into the digital domain has been carried out correctly. And so a type of equalizer can be achieved, based on derived bandpass-filters, on the basis that each bandpass-filter has been tuned correctly.

If the filters cross over at their -6db point, then one octave lower or higher, one filter will reach its -3db point, while the other will reach its -12db point. So instead of -12db, this combination would yield -15db.

The fact that the signal which has wandered into one adjacent band is at -3db with respect to the center of that band, does not lead to a simple summation, because there is also a phase-shift between the frequency-components that wander across.

I suppose that the user should be aware, that in such a case, the gain of the adjacent bands has not dropped to zero, at the peak of the current band, so that perhaps the signal will simplify, if the corner-frequencies have been corrected. This way, a continuous curve will result from discrete settings.

Now, if the intention is to design a digital bandpass filter with greater than 6 db /Octave falloff curves, the simplistic approach would be just to put two of the previous stages in series – into a pipeline resulting in second-order filters.

Also, the only way then to preserve the accuracy of the input samples, is to convert them into floating-point format first, for use in processing, after which they can be exported to a practical audio-format again. )

(Edit 03/25/2017 :

The way simplistic high-pass filters work, they phase-shift the signal close to +90⁰ far down along the part of the frequency-response-curve, which represents their roll-off. And simplistic low-pass filters will phase-shift the signal close to -90⁰ under corresponding conditions.

OTOH, Either type of filter is supposed to phase-shift their signal ±45⁰, at their -3db point.

What this means is that if the output from several band-pass filters is taken in parallel – i.e. summed – then the center-frequency of one band will be along the roll-off part of the curve of each adjacent band, which combined with the -3db point from either its high-pass or its low-pass component. But then if the output of this one central band is set to zero, the output from the adjacent bands will be 90⁰ apart from each other. )

(Edit 03/29/2017 :

A further conclusion of this analysis would seem to be, that even to implement an equalizer with 1 slider /Octave properly, requires that each bandpass-filter be a second-order filter instead. That way, when the signals wander across to the center-frequency of the slider for the next octave, they will be at -6db relative to the output of that slider, and 180⁰ phase-shifted with respect to each other. Then, setting the center slider to its minimum position will cause the adjacent ones to form a working Notch Filter, and will thus allow any one band to be adjusted arbitrarily low.

And, halfway between the slider-center-frequencies, the gain of each will again be -3db, resulting in a phase-shift of ±90 with respect to the other one, and achieving flat frequency-response, when all sliders are in the same position.

The problem becomes, that if a 20-band equalizer is attempted, because the 1 /Octave example already required second-order bandpass-filters, the higher one will require 4th-order filters by same token, which would be a headache to program… )