[SnoopyRocks]

Since I'm not sure what your background is Morsel, I won't reccomend a particular book. Try searching for "circuit analysis" on Amazon books. You'll see lots of choices. Irwin's "Basic Engineering Circuit Analysis" is commonly used in EE programs. It is not a cliff notes type thing though. This type of book will have all the basic analysis tools covered. Perhaps someone who doesn't take this stuff for granted would have a better recomendation. Don't expect an easy read.

 

[SnoopyRocks]

typo: w=2*pi*f (not 2*pi/f)

Quote:

Originally Posted by aos Well, in this case it's easy since you already have the formula for the gain of the amplifier - the ratio of two resistors + 1. Now, in this case that works for general impedances, not just resistors, so if you simply write the impedances you've got on your schematics, you get the formula immediately, in the first step. Calculating magnitude and phase is nothing but mathematics. So there was really nothing to derive here, just to write down and perhaps simplify. If you're asking where do impedances of inductors and capacitors come from, and why is the complex calculus used for steady state periodic signals, that's basic EE network theory, it should be covered in any introductory EE book, if you want to see how it's derived. But the formulas for impedance are easy to remember, Zl = jwL for inductor and Zc=1/jwC for capacitor where w = angular frequency, i.e. 2 * pi / f, and j is imaginary number one. Incidentally mathematicians use i, and EE's use j, because i is usually used to denote current intensity.

 

[morsel]

Aos, I remember the basics like Xc=1/2πfC (otherwise I would have thrown in the towel long ago instead of designing headphone amps), it's the equations Snoopy came up with that I would like to understand in more detail. Disgraceful though it may seem given my appalling lack of wherewithal, I actually have a BS in electronic engineering, it's just that I never used it.

Snoopy, "Basic Engineering Circuit Analysis" by Irwin is going for $120. Tangent recommended "Circuits and Filters Handbook" by Wai-Kai Chen, but it costs about $150 and none of the local libraries have it. My original circuit analysis book exploded 20 years ago and I never replaced it. (I'm on a tight budget.)

Now that Mathematica is behaving, everything will probably fall into place. More later after all is reexamined, verified to be in harmony with MicroCap, and optimized. Thanks again, guys!

 

[aos]

Quote:

typo: w=2*pi*f (not 2*pi/f)

D'oh, you're right. That's why the formula I had above (the long and complicated looking one) didn't work. It should be identical otherwise.

 

[SnoopyRocks]

Morsel, Irwin's book is just an example. Any of them should be fine. Try half.com for cheap version. This type of book is often sold right after the class ends, usually in as new condition. Older editions are just good as the new ones but usually come much cheaper because demand plumets when the newer editions replace them on required textbook lists.

half.com circuit analysis books

Since you do have the background I presume that all you need is a refresher and reference. This stuff hasn't changed in decades. I'd be happy to help if you want further assistance, especially since you are doing this for the benefit of the community.

 

[SnoopyRocks]

Yes, that was the error in your earlier equation. Hint: follow the units.

Quote:

Originally Posted by aos D'oh, you're right. That's why the formula I had above (the long and complicated looking one) didn't work. It should be identical otherwise.

 

[morsel]

SnoopyRocks, I massaged your equation a bit to emulate the MicroCap graph, which shows Abb. Looking good.

Now to check fc and fs.

[Head-Fi lost attachment]

 

[aos]

Quote:

Yes, that was the error in your earlier equation. Hint: follow the units.

Yep, definitely the way to go, especially in physics. What threw me off actually is that at university we used T - period - much more often than the frequency, and f = 1/T, w = 2*pi/T. So I just have a habit of seeing 2 * pi divided by *something*. f was just in the way

.

 

[morsel]

I came up with a new equation for fc based upon Abb which closely matches the Microcap graph. The numerical analysis I did years ago that we still use today provides an equation for an equivalent resistance Rc which is used to calculate fc. The Zero equation Snoopy provided is not as accurate.

I tried using similar methods to solve for fs, but it did not work out as cleanly. Time to leave for my quarterly Bay Area Carnivorous Plant Society meeting, more later.

Snoopy Zero
Numerical analysis of equivalent resistance Rc
Solve[Abb=3dB]

 

[SnoopyRocks]

Since you persist

, I derived exact equations for fc and fs. They will give imaginary values for Abb<3dB.

Quote:

Originally Posted by morsel I came up with a new equation for fc based upon Abb which closely matches the Microcap graph. The numerical analysis I did years ago that we still use today provides an equation for an equivalent resistance Rc which is used to calculate fc. The Zero equation Snoopy provided is not as accurate. I tried using similar methods to solve for fs, but it did not work out as cleanly. Time to leave for my quarterly Bay Area Carnivorous Plant Society meeting, more later.

 

[SnoopyRocks]

Validation in Matlab:

Code: BassBoost.m

Some Plots:

 

[SnoopyRocks]

Everything in one pdf file

BassBoost_ALL.pdf

 

[morsel]

SnoopyRocks, you are a gentleman and a scholar. I massaged your 3db equations and noted that your Adc is what I call Abb, which is relative to unity gain, not Av. Since I was planning to use Abb .vs. unity rather than Ao .vs. Av, I merely substituted 1 for Av, and it worked. The new fc equation plots identically to Solve[Abb=3dB]. The new fs equation works, too. Thanks again!

Zero
New fc
Numerical analysis of equivalent resistance Rc
New fs
Pole

 

[morsel]

A bit more massaging to put all these equations in similar form, and added fo to represent the 1/2 gain point where Abb < 6dB.

Zero
fc
fo
fs
Pole

 

[morsel]

Improved JavaScript uses the new equations:

 <html> <head>   <title>Bass Boost Calculator</title> </head> <body> <h1>Bass Boost Calculator</h1> <form name="bbc" onsubmit="return calculate()"> R<sub>3</sub> = <input id="R3" size="2" value="1">k&Omega;, R<sub>4</sub> = <input id="R4" size="2" value="10">k&Omega;, R<sub>bb</sub> = <input id="Rbb" size="2" value="33">k&Omega;, C<sub>bb</sub> = <input id="Cbb" size="2" value=".22">&micro;F <input type="submit" value="Calculate"> </form> <div id="output"><font color="red">JavaScript is required.</font></div> <script type="text/javascript"><!-- function format(n) {return Math.round(n*10)/10} // toFixed method not supported by Safari or IE on Mac OS X function calculate() {with(Math){ R3 = form.R3.value*1000 R4 = form.R4.value*1000 Rbb = form.Rbb.value*1000 Cbb = form.Cbb.value/1000000 Av = R4/R3+1 Abb = Rbb/(R3+R4)+1 TwoPiRC = 2*PI*Rbb*Cbb fs = Abb/(TwoPiRC*sqrt(Abb*Abb-2)) fc = sqrt(Abb*Abb-2)/TwoPiRC fo = sqrt(Abb)/TwoPiRC div.innerHTML =   "A<sub>v<\/sub> = " + format(Av) +   " (" + format(20*log(Av)/LN10) + "dB), " +   "A<sub>bb<\/sub> = " + format(Abb) +   " (" + format(20*log(Abb)/LN10) + "dB), " if (Abb > 2)   div.innerHTML +=   "&fnof;<sub>s<\/sub> = " + format(fs) + "Hz, " +   "&fnof;<sub>c<\/sub> = " + format(fc) + "Hz" else   div.innerHTML +=   "&fnof;<sub>o<\/sub> = " + format(fo) + "Hz" return false // force failure of form submission }} form = document.bbc div = document.getElementById("output") calculate() // --></script> </body> </html>