Do I understand gain properly?

[Joecool85]

I'm trying to "get" something.  Ok, Joe Davidson's Vulcan uses 3x 2n5089 trannys each with an Hfe gain of roughly 700.  Am I right in thinking this multiplies out to a gain of 343,000,000 ?  In comparing this to the gain of a LM386 at 200, does that mean I would need 3.25 LM386s (200x200x200x50) in series to get the same amount of drive?

I'm trying to come up with an idea for a metal pedal that is IC based (probably not LM386), and want at least as much gain as the Vulcan.  Am I on the right track?

[Mark Hammer]

Nope.  The track is over...here.


And you're over









here.

HFE represents a potential for gain, but that will depend upon the values of the components used in conjunction with the transistor.  Same thing for op-amps.  They don't have any gain by themselves, but have the potential for various amounts of gain, depending upon how you configure them.

When you read abut "gain" in circuits, the numbers cited are how much amplification a given stage provides, given how it is configured.

However, you ARE correct when you assume that gain is multiplicative.  If you have three stages cascaded, without interruption or attenuation, and each stage has a gain of 10, the product of that WILL be a combined gain of 1000x.

[Joecool85]

Thanks Mark, I appreciate the help.

So how does Hfe and voltage gain compare?  Do they directly compare at all?  I'm just trying to understand which has the potential for more gain, a tranny with an Hfe of 600 or an IC with a gain of 200.

[Mark Hammer]

At this point, I turn yu over to the more capable hands of other people.

[ayayay!]

This is not the best analogy, but one may think of the hFE number as equivalent to horsepower in an engine.  

A 500hp engine is fast right?  Well, no.  In a Corvette Audi S8 it's fast.  In a Caterpillar it won't lift the bucket.  In a lawnmower you'll be lucky not to get your nuts blown off.  

So it's an arbitrary number only good for relating to its application.  The right engine for the right vehicle, the right gain for the right application.  Again, NOT SCIENTIFIC, but it's really all about taste.  

[CynicalMan]

Firstly, maximum gain is not equal to hfe. Maximum gain means the highest gain that an IC can achieve. hfe refers to how the impedance between the collector and the emitter will vary in a properly-biased transistor. The transistor will set that so that the current flowing into the collector is equal to a number times the current flowing into the base. hfe is that number.

To find the gain of a transistor stage, you use the hfe in a formula that uses it among other variables to determine the gain. For example, the gain of a common emitter stage, which the stages are in a vulcan, is approximately equal to , where beta is the hfe, Rc is the impedance between supply voltage and the collector, Re is the impedance between the emitter and ground, and rπ is the internal resistance between the transistor's base and emitter (approximately equal to 0.025V divided by the emitter current).

So, looking at this formula, we can see that the gain of a transistor stage can be very high, even higher than the hfe. rπ is usually under 50 ohms and, by bypassing the emitter resistor, the gain of a stage can be set to around hfe*Rc/rπ, which can be extremely high.

[phector2004]

So technically, by changing Rc and Re in circuits, can you replace any BJT without compromising the  function of the circuit (assuming its max gain is greater than or equal to the gain in the circuit?)

Is this a formula I should write down for when I muck around with parts?

[CynicalMan]

As long as you're sticking around normal gain levels, like 100 to 1000, you should be able to compensate. If the emitter resistor isn't bypassed then hfe has almost no effect on gain. In this case, gain is approximately Rc/Re. If the emitter resistor is bypassed, however, then you have to calculate rπ to get a reliable estimate, which is a pain because then you have to calculate Ie, which means you have to go into how the transistor is biased and calculate the bias.

Another thing to keep in mind, though, is that hFE can affect bias, which can affect distortion, headroom, and operation, so you might have to figure that out as well.

This formula looks useful, but really it depends on a too many variables. If Re is bypassed, it's too complicated to figure out quickly and if it isn't,  or you might as well just estimate with gain = Rc/Re.

[deadastronaut]

post removed due to being a dumbass....

[Brymus]

They are talking about BJTs not FETs 

[deadastronaut]

whooops...

[Joecool85]

The reason all of this came up is I'd like to build a pedal with similar gain to my Danelectro Black Coffee pedal.  It uses 3 x RC4558 with a gain of 300 per channel.  Each RC4558 has two channels.  That means a gain of 729 trillion.  That would take (I think) 7 x TL071.  I'm thinking about trying to build a 2 x TL074 with a BMP style tone control after the first stage.  Should have plenty of gain, parts count might be a pain though.

[Mark Hammer]

Your estimate of the gain seems unrealistic to me.  Even though the pedal obviously has a more "intense" sound, that's waaaaaaaaaaayyyyyyyyy more gain than is required to accomplish the requisite clipping.  Even a combined gain of a few thousand is considered humungous in distortion-pedal circles.  Something is amiss.

Can we see the schematic?

[petemoore]

  If what goes in is different in voltage by X amount than what comes out of a gain stage, the voltage gain of the stage is X...

[R.G.]

Pete it on it.

The problem with saying "gain" is that you then have to say what kind it is. Transistor hfe is the current gain the raw transistor chip has, and even then it has to be qualified with what collector current, what temperature, what phase of the moon, etc. Mostly when people are talking about audio, they talk about voltage gain.

In electronics you can have voltage gain, current gain, and power gain. Power gain is just the product of the current and voltage gains a stage produces. And you can't necessarily have any of these without taking into account what load the stage is driving. If the device is driving a short circuit, the current gain is maximum, but the voltage gain is a complete loss. If it's driving an open circuit, the voltage gain is maximum, but the current gain is necessarily zero - no current comes out. And power gain is maximum somewhere in the middle of these loads.

So - you probably mean voltage gain. Hfe is current gain. These are only related by describing the rest of the circuit, including any internal feedback and any external loading.

Worse yet, you're confounding the idea of "drive" which you're probably intending to mean "how much distortion". The amount of distortion is very much tangential to the voltage, current, or power gains.

The reason all of this came up is I'd like to build a pedal with similar gain to my Danelectro Black Coffee pedal.  It uses 3 x RC4558 with a gain of 300 per channel.  Each RC4558 has two channels.  That means a gain of 729 trillion.

This is a misunderstanding of what's going on. From the TI RC4558 datasheet, the voltage gain of the RC4558 is a minimum of 20 and typically 300 volts per millivolt: that is 20,000 to 300,000. That's the OPEN LOOP VOLTAGE GAIN. They are almost never used this way. They have negative feedback which "throws away" open loop gain to get predictability. The whole point of opamps is that the gain is set by the circuit around it, not the amp itself.

The TL072 datasheet shows an open loop voltage gain of 50,000 to 200,000 typical, for comparison. Again, these are almost never used open loop.

Then there's the circuit aspect. Just because your Black Coffee uses three 4558s, there is no reason think that they're all used to multiply gain one after the other. I don't know the circuit, but I'd bet that they're used for various things, not just cascaded gain.

I'm thinking about trying to build a 2 x TL074 with a BMP style tone control after the first stage.  Should have plenty of gain, parts count might be a pain though.

You need to understand what the circuit setup does to the gain of each stage, then think about how much distortion you need, how the distortion is generated, and then how much gain is needed. Gain is NOT equal to distortion.

[phector2004]

Why are there variations in IC gain then if the open loop gain pretty much transforms any blip of a signal into Vcc+/-? Does it play an effect on noise, distortion, or other properties? Wouldn't ICs be otherwise more interchangeable in circuits?

[R.G.]

Why are there variations in IC gain then if the open loop gain pretty much transforms any blip of a signal into Vcc+/-? Does it play an effect on noise, distortion, or other properties? Wouldn't ICs be otherwise more interchangeable in circuits?

You're very close to a breakthrough in understanding.

Here's the problem. Every amplifying device ever known has variations, in gain, power, noise, everything. We do not have the technology to make identical, peas-in-a-pod amplifying devices, at least not many of them at a time. This was a problem in the tube era too. And the solution they came up with was to use negative feedback to make the gain, power, whatever, depend on a few external components that we *could* make pretty repeatable - like resistors - and to let the feedback hide what was going on inside. This was, and is, a profoundly earthshaking idea.

What it means is that if you use feedback properly, it does not matter that the IC inside the feedback loop has a gain of 10,000, or 10,000,000, as long as (a) it has enough gain to satisfy the approximations used in feedback theory, and (b) the other aspects of the internal gain and operation do not make the feedback loops go unstable. If those are satisfied, the exact gain inside the feedback loop does not appear on the outside. The excess gain over what's needed is used to hide any funny stuff inside the amplifier. And it works beautifully if you understand the limitations and approximations. So much so that for low frequencies, like audio, pretty much any opamp can be stuck in the circuit and work as long as you get the right pins in the right holes.

That condition you noted, that any blip of a signal can drive the output from rail to rail is what makes it work - the "blip" that the feedback circuit operates on is the internal error voltage. The error voltage is the output voltage you want divided by the internal gain. So if you're trying to make a +/-2V signal on the output with a gain of 10 after feedback, and the opamp has an open loop gain of 200,000, then it only takes an error voltage of 2V/20,000 = 0.01V, or 10mV of error to drive the circuit to follow the signal you want. In fact, all of the internal errors that exist are divided by the open loop gain, less the gain you use in the closed loop.

This is a profound realization; it approaches mystical if you're in the right mind set. The 16" main guns on US battleships in WWII were aimed by vacuum tube based operational amplifiers, to get elevation, range, wind effects, rotation of the earth, etc. set up so the guns could drop a shell the weight of a car in a 10 foot circle 20 miles away. You can do integral and differential calculus with analog computers based on operational amplifiers.

I'm glossing over this very, very much. But remember this: the excess gain lets you hide the imperfections behind a wall of gain, reducing the errors immensely.

[Joecool85]

Can we see the schematic?

I wish, Danelectro won't share it with me, they said it is against policy.  I guess I have a good deal of reading and learning to do yet.

Riddle me this though guys, am I totally out of the park when I think I could get similar distortion/overdrive from a single TL074?  The Black Coffee seriously screams, it makes the Obsidian seem pretty tame for reference.

If it is possible, I'm going to start doing all kinds of reading and research on op amp usage and theory.

[anchovie]

You could probably get a similar level of distortion from a TL072 - in a Boss Metal Zone there are only two opamps used in the distortion section (which ends with a pair of hard-clipping 1N4148s). The rest of the opamps are for active filtering and EQing.

Making a near-square-wave fuzz is easy. The key to a screaming distortion is how you filter/boost frequencies before and after clipping.

[stringsthings]

here's an analogy ...

the open-loop gain of a typical op amp is similar to the utmost maximum RPM of a typical car engine .... our typical overdrive/distortion/fuzz guitar stompbox usually uses an op amp with closed-loop gain .... closed-loop gain, as R.G. described, can be controlled ... when you drive your car, your RPM goes up to a certain point, and then the transmission switches to a higher gear, and your RPM goes down to a more manageable level ... ( and climbs back up again if you're stepping on the gas ) ... just as you would never want to run your car in 1st gear at the engine's maximum RPM ( which would seriously stress your engine's working parts ), you wouldn't want to run an op amp 'wide-open' ...

when you step on the gas, you're controlling RPM, which eventually translates to car speed ... miles/per/hour ...

when you turn the "drive" knob on many overdrives/distortion/fuzzbox units, you're controlling the closed-loop gain of an op amp ...