How can I calculate for dB?

[onboard]

With the talk of tinnitis over in the lounge and the state of my ears after only 10 years of rock-n-roll, I'm curious about the dB's all of our ultramegasuper high gain circuits can crank out. And how to be able to calculate a max dB for a circuit.

The only formula I could find that made sense was dB = Vg(log)20 where Vg = Vout / Vin. Is that DC? That's handy for opamp stages where the gain is a funtion of the feedback and input resistors. An opamp stage with a gain of 10 would be around +20dB, right?

But with transistor stages using something with a max hfe of 500 for example, how do you calculate actual AC gain per the circuit and then convert to dB's? Is the info lurking in the Small Signal Characteristics section of the data sheet, or is the math derived from the transistor's biasing arrangement?

I do have a textbook nearby, but I thought it might be worth bringing up here.

[R.G.]

With the talk of tinnitis over in the lounge and the state of my ears after only 10 years of rock-n-roll, I'm curious about the dB's all of our ultramegasuper high gain circuits can crank out. And how to be able to calculate a max dB for a circuit.

Don't mix up db of gain with sound loudness in db. They're different.

A decibel (db) is a power ratio. Here, read this:http://otto.cmr.fsu.edu/~elec4mus/topics/decibel.html

For acoustic power, the powers that be decided
the reference level would be the threshold of hearing at 1kz. So the faintest sound that a child (with un-blasted ears) can hear at 1kHz typically is 0db of acoustic power.

It make no sense whatsoever to say that a circuit has 100db of gain, therefore it's dangerous to hearing. Not the same things at all.

The only formula I could find that made sense was dB = Vg(log)20 where Vg = Vout / Vin. Is that DC? That's handy for opamp stages where the gain is a funtion of the feedback and input resistors. An opamp stage with a gain of 10 would be around +20dB, right?

The numbers are right. It's not DC, it's usually AC signal.

But with transistor stages using something with a max hfe of 500 for example, how do you calculate actual AC gain per the circuit and then convert to dB's? Is the info lurking in the Small Signal Characteristics section of the data sheet, or is the math derived from the transistor's biasing arrangement?

Again, you can't do it that way. First, db of gain is not db of loudness; that's like saying that 120 ohms is as dangerous as 120V. They're different.

And you cannot attribute a gain to a transistor at all in that sense. A transistor has current gain, but there is an implied circuit to even measure that. Voltage gain, which is what is usually meant by gain, is heavily dependent on the circuit. A transistor with a gain of 500 may have a voltage gain of one; or a gain of 100 with a different circuit, or a gain of over a thousand with yet another circuit. And none of these gains, even expressed as db, has any relationship to acoustic loudness.

I do have a textbook nearby, but I thought it might be worth bringing up here.

[onboard]

Decibels have caused untold confusion among AUDIO people, and most of this is due to the failure to realize that decibels are not quantities of anything and can represent only power ratios.

One step forward, three steps back...  

Given a transistor circuit stated to have 3dB of gain & that doubles the volume of the original signal, you can see how it woud be easy to mix up gain and dB loudness. And to think "Hey, I can do the math for the gain of a circuit and then figure the dB of volume increase."

It make no sense whatsoever to say that a circuit has 100db of gain, therefore it's dangerous to hearing. Not the same things at all.

Right. I thought there was a way to translate "This circuit has so much gain" into "This circuit provides this many decibles of volume increase".

I'll work on it, and remind me not to come swaggering when all I have are  incorrect assumptions :oops: Thanks for replying.

[Peter Snowberg]

If the circuit has more gain than available headroom, you will get clipping, and I know nobody here would ever want to build a circuit that would amplify "too much" and distort.  :twisted:

[R.G.]

Given a transistor circuit stated to have 3dB of gain & that doubles the volume of the original signal, you can see how it woud be easy to mix up gain and dB loudness. And to think "Hey, I can do the math for the gain of a circuit and then figure the dB of volume increase."... I thought there was a way to translate "This circuit has so much gain" into "This circuit provides this many decibles of volume increase".  

OK, that's a different context. Yes - you *can* do that, but with a lot of caveats.

As the reference I pointed you to says, db comparisons on voltage are valid if they are into the same impedance. And the voltage out of a typical audio amp does double if you double its input if it is not already clipping and if it is not driven into clipping by the increased input and if the speaker is not driven in to clipping by the increased output. If all that is true, yes, 6db of voltage gain in the front translates into a 6db greater electrical power out and, depending on frequency and speaker response, 6db greater audio output. Then you have to take into account human hearing. 6db greater acoustic power is a just noticeable increase in loudness. 20 db is an apparent doubling of volume.

I'll work on it, and remind me not to come swaggering when all I have are incorrect assumptions  Thanks for replying.

Don't be embarrassed. It's a tricky point and lots of people get it mixed up. Especially since there are conditions where xDB of gain makes for xDB bigger volume.[/i]

[onboard]

If the circuit has more gain than available headroom, you will get clipping, and I know nobody here would ever want to build a circuit that would amplify "too much" and distort.  :twisted:

That's exactly what I'm trying to avoid. Call me crazy. I want my gain clean with plenty of headroom to prevent clipping. And a little cabin, by the beach.

there are conditions where xDB of gain makes for xDB bigger volume

But not just as an expression of the circuit gain, right? So when I build something and flip the switch and shout "OMG THAT'S LOUD!!!"  - we're talking about amplitude, which is not the same as the circuit gain. Albeit both can be expressed in decibles...:?