# Equation for BJT voltage controlled amplifier

1. Feb 4, 2010

### kvtb

Hi,
as mentioned in my previous thread, I'm currently busy with a 'small' project of translating an analog device (synthesizer, based on schematics) into a digital (software) version.

I know 'nothing' about EE, I'm a Computer Science guy, so hopefully this question is not too easy :-)

This question is about how to model the behaviour of a transistor. In the analog device, a single transistor is used as a voltage controlled amplifier.
- The control voltage envelope $$V_b(t)$$ enters via the base of the transistor,
- the voltage to be shaped according to the envelope $$V_c(t)$$, enters via the collector
- the output is a voltage $$V_e(t)$$ of which was until now modeled as simply $$V_e(t) = V_b(t) \cdot V_c(t)$$

However... later I noticed that every website about transistors say that $$I_e = I_b + I_c$$, so that would imply that it is impossible to get $$V_e(t) = V_b(t) \cdot V_c(t)$$

So, my question is simply,
- given a control voltage as function of time $$V_b(t)$$
- given an input voltage $$V_c(t)$$

How do I calculate $$V_e(t)$$ in terms of $$V_b(t), V_c(t), R1, R2, R3$$ and any transistor dependent constants?

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2. Feb 5, 2010

### turin

Even if Vb and Vc are derived from ideal voltage sources, you cannot just dangle Ve like that. (Well, you "can", but I don't think that the transistor would do anything. I don't know what would happen, actually.) For instance, perhaps there is another resistor (i.e. a load) connected from Ve to ground?

BTW, what kind of transistor is it? The symbol that you have used suggests npn, perhaps 2222.

3. Feb 5, 2010

### cabraham

The 1st equation highlighted in bold is dimensionally inconsistent. You cannot multiply 2 voltages and get a voltage. Are you trying to perform an analog multiplication of 2 signals? There are circuits that do that. I would search "analog multiplier" or "Gilbert multiplier".

The 2nd bold highlight can be answered as follows. By "Ve", I presume you mean the emitter potential with respect to ground. Look up the "hybrid pi equivalent" model of the bjt operating in small signal mode. The bjt parameters are "r_pi, hfe, & gm or re". Also, r_pi = hfe/gm, where gm = Ic/Vt, Vt = kT/q. You can then compute the ac gain, i.e., Ve will be a function of Vb, the resistor values, and bjt properties. Selecting the right values for the R's minimizes the bjt parameters' influence on circuit behavior.

Did I help? A good reference text will answer your questions in detail. Horowitz is a good text.

Claude

4. Feb 5, 2010

### kvtb

turin, cabraham, thanks for your replies.

I think my question was perhaps not clear or incomplete:

turin: The schematic is just a small part of a larger schematic to illustrate my question, that's why there's no ground.
If you interested, please take a look at transistor Q65 in cell J8 of this schematic:
http://www.kolumbus.fi/janne.husu/specs/909vb.gif
The transistor in question is a 2SC2603-F (no longer in production - but the datasheets are available)

cabraham: I do not try to do (analog) multiplication of two voltages. In the software model I'm building, I incorrectly assumed that the behaviour of a transistor VCA could be approached by multiplying the envelope signal (at base) with the input signal (at collector).

I will look into the hybrid pi equivalent model to see if I can use it to model the behaviour of a single-transistor VCA.

Last edited by a moderator: Apr 24, 2017
5. Feb 5, 2010

### dlgoff

Looks like Q65 is just gating through noise from the diodes D91 and D92 with a decay envelope. Hence the rim-shot. I may be wrong however.

6. Feb 5, 2010

### turin

What's the difference? What's VCA? Anyway, that is certainly not the behavior of Ve given Vb and Vc.

BTW, the model of the transistor can be very dependent on 1) the type that you are using, and 2) the surrounding circuit connections to the three electrodes. For example, hybrid-π model may or may not be applicable. (Hybrid-π model is a small-signal model, correct?) I haven't looked at your schematic yet. I'll let you know if I can figure out what the transistor is supposed to do.

What's a rim-shot? I've never heard of such a circuit. Is this some sort of musical circuit? (wikipedia says that a rimshot is a drumming technique.)

EDIT:
Upon cursory inspection, here's how I visualize your transistor circuit:

Firstly, it can be reduced no further than:
Q65, D91, D92, R408, R415, R417, R418, R423

It has three input voltages (ultimately for collector control) and one input current (base), and it produces one output current (emitter).

The three input voltages come from three op-amps? and are presented at the three resistors: R408, R415, and R417. The three currents feed into the voltage divider circuit of R418 and R423, but the maximum input voltage to this divider is clamped by the diode circuit of D91 and D92. (Is that the right term - "clamped"?). The output of the voltage divider provides a Vc at your transistor.

Since the emitter is connected directly to a negative op-amp? input, the positive op-amp? input is grounded, and the op-amp? has negative feedback, the emitter voltage is held at 0 V.

So, the three input voltages basically control Vce (subject to the diode clamp constraint), without negative emitter feedback. The output of the transistor is a current output that flows through the op-amp? feedback RC circuit.

With the given Vce, the output current is basically determined by the input current at the base. This current comes from Q64 through two resistors: R401 and R403. I think that these resistors are mainly for filtering and feedback to Q64.

So, this looks like a base-to-emitter current amplifier circuit that is somehow controlled by three voltages (which somehow work together to determine the current amplification by controlling Vce). I don't know if the diode circuit is just for protection, or if it has a functional purpose.

Last edited: Feb 5, 2010
7. Feb 5, 2010

### dlgoff

The circuit looks to be an electronic drum (percussion) set. It looked like the diodes were involved in making the noise (used to simulate snare durms) but I'm not sure since there is also a "noise section" in the circuit. Here is a way to generate and amplify thermal noise from a diode:

The three wave forms, F1, F2 and F3 are the envelopes used to modulate the noise. Which makes the sound of a rim-shot. i.e. the stick strikes the head and rim of the snare drum at the same time.

Last edited by a moderator: May 4, 2017
8. Feb 6, 2010

### kvtb

dlgoff, turin, thanks for your replies.

let me try to explain the circuit in the link I've given, using another link;
http://mitglied.multimania.de/raf909/rimshot.htm

the three op-amps and surrounding capacitors and resistors are sine wave generators, these generate a sine wave (at three different frequencies) with different damping.

the three sines are then mixed together, and 'wave shaped': the two diodes are 'limiting' the amplitude of the mixed signal.
(In other parts of this schematic, you'll also see this construction with these two diodes. For example, to 'translate' a triangle wave into a 'sine' wave. So these diodes are not related to noise generation).

For those who have LTspice installed, and are interested in the output of the Rimshot circuit, please load and simulate the attached file. In the LTSpice file, you'll see transistor Q3, which is the transistor that does the VCA.

You may want to 'probe' the following nets:
F1, F2, F2 (to see the sine waves)
shaped (effect of the two diodes, and input to the collector of the transistor)
ENV ( the envelope applied to the base of the transistor)

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9. Feb 6, 2010

### dlgoff

I stand corrected.

10. Feb 8, 2010

### turin

Can you describe the "trigger"? I'm most curious about the amplitude of the trigger (above ground). I imagine that it is just a quick square voltage pulse of several volts amplitude (above ground) that is produced by a key press or something. I don't want to know where it comes from, just what are its expected characteristics.

11. Feb 10, 2010

### kvtb

Hi, the trig signal is a +5V pulse, duration is 2 ms

BTW, in mean while, I've tried to 'measure' a transfer function (as function of Vb and Vc) and tried to fit an equation on top of it. I'll post results later.

12. Feb 10, 2010

### turin

OK. That's what I expected. I don't think I can offer any further input.