# How do I calculate resistance across the transistor in this circuit?

#### Green Bean

Joined Mar 31, 2017
126
I have designed this circuit using a 555 that allows you to control the frequency of the pulse wave output with four switches. Here is a link to an online simulation of the circuit: http://tinyurl.com/yd6mdnc6

In the circuit, the transistor is used kind of like a variable resistor. My question is, with the transistor in the configuration shown in the circuit, how do I calculate the resistance across it? (As if it were, in fact, just a resistor.)

#### crutschow

Joined Mar 14, 2008
23,378
That is a rather strange 555 circuit. I really don't see what the transistor is doing or why it is needed.
To change the 555 frequency all you need is a resistor on each switch position.
• Remove the transistor.
• Remove the diodes.
• Remove the 1k resistors.
• Connect the string of 10k resistors between the dis and /tr terminals.

• Green Bean

#### Green Bean

Joined Mar 31, 2017
126
That is a rather strange 555 circuit. I really don't see what the transistor is doing or why it is needed.
To change the 555 frequency all you need is a resistor on each switch position.
• Remove the transistor.
• Remove the diodes.
• Remove the 1k resistors.
• Connect the string of 10k resistors between the dis and /tr terminals.
Oh yeah, duh. No clue what I was thinking there. But then, how is a transistor used as a variable resistor, and how do I calculate the resistance across it?

#### crutschow

Joined Mar 14, 2008
23,378
But then, how is a transistor used as a variable resistor,
A BJT has a high-impedance collector and basically outputs a constant current.
It cannot be readily configured as a variable resistor.
Why did you think it could be?

#### BR-549

Joined Sep 22, 2013
4,936
If I gave you a blank resistor........how would you determine the resistance?

#### EM Fields

Joined Jun 8, 2016
583
Oh yeah, duh. No clue what I was thinking there. But then, how is a transistor used as a variable resistor, and how do I calculate the resistance across it?
By measuring the collector-to-emitter voltage and the collector current at a given base current and dividing the collector-to-emitter voltage by the collector current.
The quotient will be the calculated dynamic collector-to emitter resistance at that point.

#### crutschow

Joined Mar 14, 2008
23,378
The quotient will be the calculated dynamic collector-to emitter resistance at that point.
That's more like the static equivalent resistance.
To get the dynamic resistance you would need to slightly vary the collector voltage and measure the corresponding change in collector current.
Dividing the change in voltage by the change in current will give the dynamic resistance (which will likely be considerably different than the calculated equivalent static resistance).

• OBW0549

#### MrAl

Joined Jun 17, 2014
6,513
Hi,

Transistors can be used as variable resistors, it's just not that easy to control. You have to establish a relationship between the drive and the output or use feedback. In fact, the original name (from what i read) came from a variation of 'resistor' or 'varistor' in some way. And hopefully you can put up with any temperature variations as they affect the transistor parameters.

Yes the simplest method to figure out the equivalent resistance is to measure the collector voltage Vc and the emitter voltage Ve and subtract: V=Vc-Ve, and then measure the current through the collector Ic. The approximate resistance (neglecting the base current) is:
R=V/Ic.

This will work in some cases and not others so there are a lot of conditions that have to be met. More commonly though we'll see an FET used for that purpose.

It is also not clear why you have a transistor in the circuit anyway if you already have switches that change the resistance. Normally you would want a variable resistance that varies with some input voltage so you can change the voltage and get a different resistance even if it doesnt show a perfect relationship between voltage and resistance. In other words the design is most likely too complicated for what it has to do as Crutschow had mentioned.

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#### Green Bean

Joined Mar 31, 2017
126
Hi,

Transistors can be used as variable resistors, it's just not that easy to control. You have to establish a relationship between the drive and the output or use feedback. In fact, the original name (from what i read) came from a variation of 'resistor' or 'varistor' in some way. And hopefully you can put up with any temperature variations as they affect the transistor parameters.

Yes the simplest method to figure out the equivalent resistance is to measure the collector voltage Vc and the emitter voltage Ve and subtract: V=Vc-Ve, and then measure the current through the collector Ic. The approximate resistance (neglecting the base current) is:
R=V/Ic.

This will work in some cases and not others so there are a lot of conditions that have to be met. More commonly though we'll see an FET used for that purpose.

It is also not clear why you have a transistor in the circuit anyway if you already have switches that change the resistance. Normally you would want a variable resistance that varies with some input voltage so you can change the voltage and get a different resistance even if it doesnt show a perfect relationship between voltage and resistance. In other words the design is most likely too complicated for what it has to do as Crutschow had mentioned.
Ok, thanks.

#### Green Bean

Joined Mar 31, 2017
126
Like I said, I have no clue what I was thinking, here is a redesigned version of the circuit: http://tinyurl.com/y9ecgq5d

I the output is now used as a clock signal for a digital counter. I did this because (1) the 555 usually outputs an ugly pulse wave, now there are four nice square waves, and (2) there are now four "octaves" (this is a little synthesizer). But if I wanted to build this in real life, what would I need to do to put this signal out to a speaker?

And, how (besides what I've already done with the counter to get actual square waves) can I get nicer sound than the usual "tinny" sound from most 555 timer circuits like this:
(Although I should say that I don't think there is anything wrong with the people making these circuits, I think it's just that they aren't that concerned about the sound quality.)

I have heard a bit about amplifier circuits (many using the LM386 amplifier) but a lot of the videos and things I saw said that other schematics were wrong, or that there were easier ways to do it and all this- I really don't know what to think. I also should say that I have an 8 ohm, 0.5 watt, 3x3 inch speaker that I'd like to use. I'm not sure if I can really get "great" audio quality from that, but what's the best I can do?

#### crutschow

Joined Mar 14, 2008
23,378
Yes the simplest method to figure out the equivalent resistance is to measure the collector voltage Vc and the emitter voltage Ve and subtract: V=Vc-Ve, and then measure the current through the collector Ic. The approximate resistance (neglecting the base current) is:
R=V/Ic.
I hate to beat on this, but that value is not an ohmic resistance.
It's just the equivalent resistance at a static point, and is unrelated to the ohmic resistance.
The transistor collector looks like a current source with an an impedance of hoe (the flat portion of the characteristic curves below).
The hoe ohmic resistance is typically several kΩ to tens of kΩ depending upon upon the collector current. Last edited:
• OBW0549

#### MrAl

Joined Jun 17, 2014
6,513
I hate to beat on this, but that value is not an ohmic resistance.
It's just the equivalent resistance at a static point, and is unrelated to the ohmic resistance.
The transistor collector looks like a current source with an an impedance of hoe (the flat portion of the characteristic curves below).
The hoe ohmic resistance is typically several kΩ to tens of kΩ depending upon upon the collector current. Hi,

Yes, what you say is true and i agree, but that's not a complete picture of what resistance is.
Resistance itself does not have to be ohmic. It's only when we need a linear resistor that it has to be ohmic. We can easily make a non linear resistor with a transistor, but our circuit has to be able to deal with that non linearity, and that non linearity may be great or small, and if it is small relative to the application, we've got what we wanted, which is a resistive element even though not an ohmic element.

This is one reason why those "What is Ohms" threads go on so long, because we have to be able to classify an ohmic resistance vs just a plain resistance, and when people first learn about this they have a hard time distinguishing the two from one another probably because they are both measured in Ohms.

Let me try to give a couple examples.
First, if we have an oscillator circuit that is working at 1kHz with a 10k resistor in a certain place, i am sure you agree that the 10k resistor is ohmic because after all it's a regular 10k resistor maybe 1 percent tolerance. Now we disconnect the 10k resistor and plug in instead a 5k resistor and the frequency rises to 1.5kHz, then we disconnect the 5k and plug in a 2.5k and the frequency rises to 1.7kHz.
Now we did not get a linear change in frequency with change of resistance, but we did in each case have an ohmic resistor in the place that mattered the most for the adjustment of the frequency. But can we say that any resistor was not resistive? No we cant.
Second, replace that resistor with a transistor (assuming the biasing could handle the polarity) and vary the base current. We get a very non linear response in frequency with base current BUT the oscillator works the same as before. We still get various frequencies out of the oscillator and they tend to vary in a way that matches the resistors we used previously IF we adjust the transistor base current accordingly.

The only difference as i mentioned is that the transistor will not make a super stable resistance like the resistors will because of temperature variations and bias variations which can even come from the AC component of the frequency itself, so it could cause some distortion, but that depends on how much the amplitude varies, and some distortion may be acceptable even in a sine wave oscillator, and if it is a square wave oscillator then it may not matter at all and then we only need be concerned with the change due to temperature.

So i agree it is not a linear 'ohmic' resistance, but it still functions as a resistance, which was my point. Of course it it needs to be a linear resistance over a wide range of operation, then it may not be a good idea depending on the application. Sine wave apps are more sensitive to non linear elements for example.

So your point is a good one because we need to be aware of the difference, but it's not the only way we need to look at this because non ohmic resistance is also useful.

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