Choosing R-C Combo for High/Low Pass Filter Question

[rocket8810]

Hey guys, I've been reading a lot about high/low pass filter creations and I just have such a hard time trying to understand how to find the "right" values for the resistor and cap. I've read three different electrical engineering books, read multiple forum posts, searched other sources online and I'm missing something and it doesn't sink in. Here are my questions:

1: Mostly I'm designing pedals for bass rather than guitar, so in order for a high pass filter to let the frequencies through that I want I know that I need to increase the size of the cap in relation to the resistor. I want to make sure I can tune to a low C and not lose any low end, so it needs to reach i think 32Hz. I used the AMZ R-C calculator and figured out that I can use a combo of a .47uF cap and 10k resistor, but I can also achieve the same frequency by using a .0047uF cap with a 1M resistor. Which would be a better choice? I ask, because I know that the bigger the cap I use the more low frequencies can pass, but according the the calculator I achieve the same frequency response with both combinations. So in a nutshell how does the size of the cap affect in relation to the resistor affect a low pass filter?

2: I've been wondering is it possible to change a high pass filter to a low pass filter? And more importantly, when is one better to be used? I understand that low pass filters essentially cut the high frequencies, while the high pass filter essentially cut the lows, but is there a time when one is more optimal then the other?

[R.G.]

Hey guys, I've been reading a lot about high/low pass filter creations and I just have such a hard time trying to understand how to find the "right" values for the resistor and cap. I've read three different electrical engineering books, read multiple forum posts, searched other sources online and I'm missing something and it doesn't sink in.

The fundamental relationship of a single-r, single-c filter is taken from the analogy of a voltage divider. A resistor is a fixed amount of impedance to current flow for all frequencies. A capacitor's impedance decreases with frequency. If you make a voltage divider from a resistor and a capacitor, there are two ways to do it: resistor on top, cap to ground, and cap on top, resistor to ground.

If you start with a frequency near DC and increase frequency into an R-C voltage divider, you get either a high pass or a low pass, depending on whether you put the cap on top or the resistor on top.

A capacitor is nearly an open circuit at near DC, and becomes nearly a short circuit at some high frequency.  So if the capacitor is on top of the voltage divider, at very low frequencies, the cap looks like an open circuit, and the output of the divider is nearly zero. At high frequencies, where the impedance of the cap has become much smaller than the resistor on bottom of the divider, the capacitor's impedance is insignificant compared to the resistor, and all higher frequencies go through at about the same level. This setup blocks lows and lets highs through, so it's a high pass filter.

If you reverse things and put the resistor on the top of the divider and the cap on the bottom to ground, then at very low frequencies, the cap looks like an open circuit, much higher impedance than the resistor, and signal goes through almost unchanged by the R and C. At very high freuqencies where the capacitor's impedance is much smaller than the resistor, the capacitor "shorts out" the signal on the output. This is a low pass filter.

In both cases, the point where the signal is divided in half by the R and the C is the frequency where the cap's impedance is the same as the resistor's value. In algebra terms, X_c =R.

We know X_c = 1/(2*pi*F). so the frequency where the cap is equal to the resistor impedance is F = 1/(2*pi*R*C). That's true for either high pass or low pass. The product of R and C for such a filter is also called the "RC time constant" as it has units of seconds.

To repeat: The half-voltage point of any single-R, single-C filter is F = 1/(2*pi*R*C). Period and end.

1: Mostly I'm designing pedals for bass rather than guitar, so in order for a high pass filter to let the frequencies through that I want I know that I need to increase the size of the cap in relation to the resistor. I want to make sure I can tune to a low C and not lose any low end, so it needs to reach i think 32Hz. I used the AMZ R-C calculator and figured out that I can use a combo of a .47uF cap and 10k resistor, but I can also achieve the same frequency by using a .0047uF cap with a 1M resistor. Which would be a better choice? I ask, because I know that the bigger the cap I use the more low frequencies can pass, but according the the calculator I achieve the same frequency response with both combinations. So in a nutshell how does the size of the cap affect in relation to the resistor affect a low pass filter?

It's always the same: double the C, lower the frequency of rolloff by half. Period and end.

By the way, I think that using online calculators can permanently cripple your ability to understand what's going on. The calculator becomes a crutch you never let go of.

One complication you're having is that you don't know the resistance that matters in your circuit. When you say "the resistor", where is that in your circuit? If it's an input, you need to know what the resistance of the entire, combines input to the amplifier you're coupling to with the cap. Sometimes you don't get to choose the resistance you're seeing into an amplifier input. If the input impedance of the amplifier is 10K (which is very, very low for guitar or bass inputs and will cause treble loss on its own, for other reasons), then the cap that gives half voltage passed at 32Hz is C = 1/(2*pi*F * R) = 1/(6.28*32*10k) = 0.497uF. If the input is 1M impedance, the cap is 100 times smaller, or 4.97nF.

=>> You may or may not get to pick what the resistor is in the equations. <<=

You may have to fit the cap to the resistance/impedance combination that's already there.

Here's another quirk to remember. F = 1/(2*pi*R* C) is the half-power point. That's where you've already lost half the audio power the signal would otherwise have had. If you want no significant losses at that frequency, you have to move the half-power point much further away. For instance, if you want no significant losses at 32Hz, design for 3.2Hz to ensure you have minimal losses at the lowest frequency you want to pass.

2: I've been wondering is it possible to change a high pass filter to a low pass filter?

Yes. You can easily enough design a single-R, single-C to be a high pass or low pass, and at the same half-power point. Just invert the R versus the C.

And more importantly, when is one better to be used?

If you want to pass highs, use a high pass. If you want to pass lows and cut highs, use a low pass.

I understand that low pass filters essentially cut the high frequencies, while the high pass filter essentially cut the lows, but is there a time when one is more optimal then the other?

Sorry, I'm really having trouble understanding what  you mean. It's up to you in designing circuits to know what you want the sounds to be, whether you want more or less highs or lows. Once you know, you pick the approach you want.

I must be thick tonight, but your question translates to me as much the same as asking whether a bicycle is better than a canoe. Well, it all depends on what you want to do. "Optimal" means "best in some measurable way", and there isn't any better or best in frequency shaping until you decide what you want to do.

If you mean something like "is it better to get more lows by boosting lows or cutting highs?", then there are answers, but again they depend on other things in the circuit than the R and C you're picking for the filtering.

[rocket8810]

R.G. you're the man. A lot of what you said makes more sense for some reason, I really thank you for that. What i mean about when is it optimal to use a high pass over a low pass comes from the idea of modifying a pedal to accept lower frequencies. A lot of what I've read has always been just increase the input cap or the cap for the filter and you'll be good, but it never made sense to me because there wasn't much more explanation than that. I've been trying to design my own circuit for bass, and when I think of what I want the sound to be like, I know I don't want to lose any highs for fear of loss of clarity, but still want there to be a lot of low end. With that in mind I would think a high pass filter set to cut the low frequencies rather than high frequencies would make more sense. I guess in my head, I would think that low pass filters could have the risk of getting muddy, with cutting the treble. Hence, the question of when is it optimal to use one over the other. I know that you can combine the two, as I've read on geofex, AMX, and Beavis.

Also, thinking about the question of one filter being optimal over the other, is there a good place to learn more about toneshaping using filters?

To put this more into context, what I'm working on has two stages, first a MOSFET booster based on the AMZ MOSFET booster, into a germanium booster stages that's a modified rangemaster, like the Beano boost. I know that the rangemaster is a treblebooster by design, but  love the sound it produces, and after reading the info on geofex and know the Beano boost works beautifully with a bass, I'm trying to determine the filter from the MOSFET stage to the Ge stage to ensure that I can keep the low end, and have clarity. There is not going to be a tone know, just an output knob, which makes the filter design really important.

It's my first time designing, and I want to do things properly instead of screwing around not understanding what I'm doing. I'm going to breadboard everything once I figure out the schematic, and I can play with the values. I know this is a noob question, but I'd rather get help from people who have more knowledge and ask so that I can learn. Any more advice and guidance would in incredible.

[GibsonGM]

R.G. will be back to discuss how to determine which method is 'best'....one thing I'd chip in while we wait is the thought that....isn't using higher resistances noisier?  <<thermal noise>>   

So that probably has much to do with the thought of "just increase the input cap", as well as the constraints already mentioned caused by input impedances and the like.

Great "article", R.G.!   

[chptunes]

Great info.  ..if the original poster doesn't mind, I've been wondering about the relationship of Resistors and Caps in the Bias position.  Like R5 and C6 in this Mini-Booster.  Do they behave as a High Pass Filter?  Is the Corner Frequency calculated in typical fashion?

Thanks..

http://www.muzique.com/amz/mini.htm


imag

[rocket8810]

If my understanding of filters is correct and if you pay attention to what R.G. said is that you need to think if both high and low pass filters as frequency dependent voltage dividers. That means you have a resistor and capacitor in series to ground. The difference is the position of the resistor and capacitor. In high pass filters the resistor is to ground and in low pass filters the capacitor is to ground. Anyone correct me if I'm wrong.

[R.G.]

OK, Rocket, I understand your objectives better.

As an aside, you have the right attitude to leaning this. There's a lot to learn, but you'll get there if you keep working at it.

Simple one-R, one-C networks are easy enough to get an understanding. But I remember being baffled about how that related to the throng of parts in a real circuit. The clue to understanding this came in two forms. One was in a networks class where we got the idea of equivalent networks - a simplified version of Rs, Cs and Ls with fewer parts that acted the same way electrically as the original network. The other was in a circuits class where we had to calculate the input and output impedances of simple circuits.

The equivalent-circuits thing was a biggie: for more info, look up Thevenin and Norton equivalent circuits. A Thevenin circuit reduces a circuit to a voltage source and a series resistor which has the same response as a voltage source and many resistors. It is possible to calculate this, often by inspection. For instance: A 9V battery feeds a 10k/10K divider; what is the Thevenin equivalent circuit?

By definition, an equivalent circuit will have the same open circuit voltage and short circuit current as the original circuit. In this example the open circuit voltage at the output is just the voltage-divider voltage of 4.5V. The short circuit current is 9V divided by 10K. Through some algebra, it's possible to show that the Thevenin equivalent voltage will be the voltage divider output voltage, and the series resistance will be the parallel combination of the resistances, or 5K in this example. So the 9V/10K/10K network acts exactly the same at its output as a 4.5V source with a 5K resistor in series with it.

The Norton equivalent circuit is a current source in parallel with a resistor. The Norton equivalent circuit has the same short circuit current as the original network, and the same open circuit voltage. So in our trivial example, the Norton equivalent would be 4.5V/5K for the current source, in parallel with a 5K resistor to generate the 4.5V equivalent open circuit voltage.

Here's the big deal: you can transform a Thevenin into a Norton and back again, just by inspection, and you can collapse a wad of parts into one Thevenin or Norton, then combine other parts with them to simplify much bigger networks. A lot of what I was doing in "The Technology of the Tube Screamer" for instance, was based on doing these Thevenin/Norton conversions, a lot of them in my head. You can condense a voltage source, some parallel and series resistors and so on into one voltage (or current) source and one resistor, then use that resistor to calculate frequency response when you hit a cap.

This is good because the input and output impedances of most circuits have an active device, then a bunch of parallel and series resistances. The active device itself is usually something that can be modeled by a voltage source or current source and an internal parallel or series resistance. A bipolar transistor collector or FET drain is often best modeled as a current source (or sink), for instance. The resistor connected to it converts this current to a voltage, and is very close to the series impedance of the device's output in that circuit. The input impedance of an active device is the input impedance of the device itself, in parallel/series with the biasing resistor networks. 

By repeated use of Thevenin/Norton conversions, you can boil down nets of many resistors to one or two. Then you can use the simple one-R, one-C filter calculations to estimate the frequency responses.

What i mean about when is it optimal to use a high pass over a low pass comes from the idea of modifying a pedal to accept lower frequencies. ...I've been trying to design my own circuit for bass, and when I think of what I want the sound to be like, I know I don't want to lose any highs for fear of loss of clarity, but still want there to be a lot of low end. With that in mind I would think a high pass filter set to cut the low frequencies rather than high frequencies would make more sense. I guess in my head, I would think that low pass filters could have the risk of getting muddy, with cutting the treble. Hence, the question of when is it optimal to use one over the other. I know that you can combine the two, as I've read on geofex, AMX, and Beavis.

As a concept, there is often a "mid-band" response, that range of frequencies where signals come in, get amplified and go out, without the frequency-modifying effects of reactive components entering into it much. In these frequency ranges, the high pass and low pass effects are not causing much if any change to the output signal. At both much lower frequencies and much higher ones, the filtering effect of reactive parts causes gain changes.

For instance, if you have a circuit with a MOSFET as an amplifying device and a bias network that reduces to about 100K through equivalent-resistor techniques, and an input cap, you can set the lowest frequencies that will get in by picking the value of one input capacitor. Using your 32Hz example, we need at least C = 1/(2*pi*100,000*32) = 49nF to get down to 32Hz at half-power, or something much bigger for almost no loss at 32Hz. This cap has little if any effect at frequencies above this, and can be ignored as input signals move further up into the mid-band. It has no way to cut highs in this circuit. Likewise, there will be an output capacitor to block the DC from the device's drain from affecting succeeding stages. This cap has to be chosen based on the input impedance of the stages that follow this one.

So how are highs changed at all? In this circuit, they are not, at least not in the audio band. You have to put in other filtering parts to change frequencies above the incoming high pass. Note that the incoming HIGH pass has the effect of determining the LOWEST frequencies you will get in. If you want to roll off highs, you can pick several places to do it.

"Muddy" and "clarity" are -forgive me- muddy issues. "Muddy" is usually used when there is so much bass that modest distortion causes the effect of covering up much of the high frequency detail. "Clarity" is often taken to be either loss of treble, or having it covered up. However, "warm" is used when people LIKE some loss of treble or boosting of bass. A good designer will avoid thinking of sound in these terms until they go to do their advertising, and instead think of what the frequencies are where the frequency response changes in the audio band, then relate those to the vernacular terms for "bass" "mid" "low-mid" "high-mid" "presence" "treble" "edge" "sheen" "grit" "grak"...

If you want bass to come through, use a high pass filter. Everything higher than X will come through relatively unscathed. If you want ONLY treble coming through, use a high pass filter. Everything above Y will come through. The only difference is that X is a lower frequency than Y. If you want bass above X, but to cut off treble above Y, you use a high pass filter to let X through, but X is a low number, maybe 32Hz. Then you use a low pass filter to cut off everything above Y, but Y will be, perhaps 7kHz. You use two filters one after the other, to get everything above 32 but below 7kHz. In the middle is that "mid band" where the amplification is unaffected by filtering.  You use multiple filters, one after the other, to affect different frequencies.

It is possible to combine high and low pass ( and mid pass or cut!) filters into the same net, but it can be challenging to get them all to work as you want without interacting with each other. Pros will tend to use separate filters wherever they can, to get the extra control and lack of confusing interactions.

Also, thinking about the question of one filter being optimal over the other, is there a good place to learn more about toneshaping using filters?

The best single-capsule place is "The Active-filter Cookbook" by Don Lancaster. You can usually get these at Amazon. Often used copies are quite cheap. I keep a copy in my bookshelf, and still refer to it some 20 years after I bought my copy. I think I wore one copy out and bought another at one point.

To put this more into context, what I'm working on has two stages, first a MOSFET booster based on the AMZ MOSFET booster, into a germanium booster stages that's a modified rangemaster, like the Beano boost. I know that the rangemaster is a treblebooster by design, but  love the sound it produces, and after reading the info on geofex and know the Beano boost works beautifully with a bass, I'm trying to determine the filter from the MOSFET stage to the Ge stage to ensure that I can keep the low end, and have clarity. There is not going to be a tone know, just an output knob, which makes the filter design really important.

The Rangemaster circuit is a simple amplifier, with an input impedance determined by the input impedance of the transistor and its emitter resistances, in parallel with any biasing and pulldown resistors used. It is a treble booster only because it uses a very small input cap as a low pass filter, cutting off frequencies below some mid-range level. See http://www.geofex.com/article_folders/rangemaster/atboost.pdf for my original writeup on the Rangemaster. As an aside, I was threatened for putting that on the web. One early pedal maker had a rangemaster and was selling copies; he didn't like that I was putting it out for everyone. That article is the first to put the Rangemaster circuit out on the web. But I digress. 

One quirk of simple one-R, one-C filters is that they don't cut off very fast. So we say that they have a cutoff at 100 Hz or 10kHz or whatever. But in fact, that is the frequency where the power is down by half, and it declines by half the power with each increasing (or decreasing) octave.  The Rangemaster uses this long, slow decline to favor treble over bass. So when you change the value of the input cap on the simple Rangemaster circuit, you are moving the long, sloping range of decreasing frequency response up and down. In your case, there are two ways to approach it, a simple one and a more complicated one.

The simple one is to just dink with the value of the input cap and see what sounds good to you. Generally, making that cap bigger  (and possibly making the output cap bigger by the same amount so some of your signal goodness that got in the input can get out the output!) will increase the amount of bass getting in. It will also make the turnover point where treble seems to be boosted lower. This simple approach may be good, may not. Your ear knows what it likes. And this is what the advice you're getting about "double the input cap" comes from.

A more complicated way that may be more what you like is to stop the loss of bass at some point. This might take the form of a capacitor and resistor in series that parallels the original input cap. This cap would be much bigger than the original input cap, so it "passes" much lower frequencies; the resistor limits how much of those lower frequencies it can pass into the circuit, and so with the original input cap choking off signals below X, the new R+C lets through a fixed "floor" of signal, so that the bass loss stops at some point and you can ensure that at least this amount of bass comes through. This new R+C is both a high pass with the input impedance of the Rangemaster circuit, and a low pass with the R and the original C to counteract the original C's ever-increasing bass loss in the original circuit.

There are many ways to do things like this. They all come down to the change in impedance of the caps you use with frequency, the resistors involved, and where the capacitors' impedances become so big or small with frequency that they can be assumed to be open circuits or short circuits compared to the resistor.

There are exact, sixteen-equations-in-sixteen-unknown ways to solve these. I always hated matrix algebra; I could get to a usable answer while the other guys were setting up the matrixes. My answers were never exact, but boy were they fast, and usually good enough.

[PRR]

> Resistors and Caps in the Bias position.  Like R5 and C6 in this Mini-Booster.  Do they behave as a High Pass Filter?  Is the Corner Frequency calculated in typical fashion?

"Cathode bias". We don't call it a cathode on a BJT or FET, but it is the same thing.

Complication: there's a resistance inside the device. "Looking into the cathode (emitter, source)" we see a resistance.

For tubes and FETs, we can assume this resistance is (usually! with serious exceptions!!) about equal to the bias resistor. Therefore the R-C product is about half, and the bass cut-off about an octave up. Here, say -3dB@34Hz (which as R.G. sez means some-weakening by 68Hz).

For BJTs, use Shockley's Equation. Or figure 30 ohms at 1mA, higher at lower currents.

Additional BJT problem: the R-C in the emitter reflects out to the Base terminal. And you almost always have another R-C network there. They interact. The only "Sane" approach is to make the emitter cap Much-Much-Much bigger than it needs to be, and find your bass roll-off in the Base network.

470uFd against 30 ohms is -3dB@12Hz. This is low-enough for many audio purposes.

470uFd is BIG. Even though typically under 3V, it is bulk and cost. In mini-work it is tempting to downsize the emitter cap to dump any excess bass.

A "great" emitter bypass will give Too-Much Gain for any sane (non-distorting) purpose. We often stack a hundred ohms or so in series. Now the resistor is "most of" the R in the network, we don't have to figure emitter internal resistance, we don't need such a huge cap.

[PRR]

> I always hated matrix algebra; I could get to a usable answer while the other guys were setting up the matrixes. My answers were never exact, but boy were they fast, and usually good enough.

You can SPICE and let the idiot set-up the matrices. Of course when it gives you silly answers you don't know if they are right, or you did something wrong, something that will take much longer to find than it did to set-up. (Older SPICE is prone to m vs M mix-up.)

You would not like Kuehnel's Bassman 5F6a book. He analyzes a classic stage amplifier using matrices and Cramer's Rule. I never heard of this Cramer; turns out it is a computationally intense method that was "useless" until computers. Funny thing about math though: you should always get the same answers, and since all input for tube-amps comes from tracing old-old hand-drawn curves (and real tubes vary +/-20%), great precision is impossible. Two thumbs, one sheet paper, and occasional calculator, I quickly confirmed all his results up to page 141 (where his computer lost a square-root sign).

Picking BJT emitter caps (with no series resistor) is the only place I'd use more than a matchbook cover. Here I go with Cherry-Hooper.... if it matters, make the cap BIG. Sub-Hz if your budget allows.

[tubegeek]

Cramer's Rule. I never heard of this Cramer; turns out it is a computationally intense method that was "useless" until computers.

Kind of off topic:
It's interesting to me that you two, both so very analytical and sensible thinkers about electronics, express so much frustration/impatience with matrix algebra. It's interesting because matrix algebra is exactly where I gave up on math in college myself - I started my undergrad as a physics major and the field required a parallel study of math in order to support the physics.

(As an aside to an aside, it took quite a while in the history of science before physics and math were even regarded as separate topics. To say that math "supports" physics is not really how it works - it's more accurate in my estimation to say that physics is a series of demonstrations of how the properties of mathematical objects play out in the world of tangible objects.)

I wasn't able to keep up my studies in Social Zoology (i.e., party animalism) and math and physics simultaneously... it was Matrix Algebra (in combination with my especially demanding independent study of Social Zoology, of course) that did me in. Of course, it didn't help that it was taught in a completely theorem-proof, theorem-proof fashion with not even the slightest hint as to why the subject could possibly be of any use, but that wasn't why I couldn't hack it. I ended up switching majors and I regret it to this day.

[rocket8810]

Thanks R.G. I swear if I had even half the knowledge as you have lost on circuit building I would be a pro by now. I think I get what you were trying to explain about the Thevenin and Norton equivalence circuits, and started watching some lectures and reading more about them, not to mention I just ordered "The Active-filter Cookbook." Hell, if you still use it and wore it out I must add it to my small, yet growing library.

Now it's funny you mention your article about the rangemaster, because I've actually before, and really helped me understand it better. And actually through my research about it I found a modified version for NPN, and some added features to protect the transistor from fuzz central, called the rangeblaster. Here's the schematic:



But, after rereading it there's something else that I've had trouble understanding with. I know that in your dissection of the rangeblaster you mention the HFE should be between 70-100, what if a transistor was used with a larger. I have a few different Ge transistors that I have to check for leakage and HFE that I got from Steve at smallbear, I think they were ETCO NPN Germanium 2N1306's. He suggested them when I told him about the direction I'm going with this design, as they have low leakage, and high HFE for NPN Ge transistors. But, the more I read about the rangemaster, it seems the HFE matters a lot. So I guess what I'm getting at now, is what is the role of HFE a circuit? If you change the transistor for a lower or higher HFE how will it affect the circuit? Does it affect the bias?

I swear every question leads to answers, that them bring up more questions it can be maddening.

[R.G.]

(As an aside to an aside, it took quite a while in the history of science before physics and math were even regarded as separate topics. To say that math "supports" physics is not really how it works - it's more accurate in my estimation to say that physics is a series of demonstrations of how the properties of mathematical objects play out in the world of tangible objects.)

From my recreational reading, I have begun to suspect that math is the real, underlying topic, and that physics all comes out of the math, not the reverse. It is possible that when God said "Let there be light..." it was really a set of 26-dimensional equations, not a statement.

Of course, it didn't help that it was taught in a completely theorem-proof, theorem-proof fashion with not even the slightest hint as to why the subject could possibly be of any use,

One the things I did not like about matrix math is that it completely obscures the underlying phenomena it purports to describe.

I could regurgitate enough of the stuff to pass the tests, but I never LIKED it. I don't think I've ever set up a matrix to solve a problem in my practice or hobbies, and I've done many, many hours of algebra and calculus along the way. As an oddity, look up the programming language APL. Matrices are fundamental math structures in APL. I did like solving many-channel digital signal processing in APL. But by subsuming the entirety of the matrices into an equation form, something about the reality came back in my mind anyway.

But, after rereading it there's something else that I've had trouble understanding with. I know that in your dissection of the rangeblaster you mention the HFE should be between 70-100, what if a transistor was used with a larger. I have a few different Ge transistors that I have to check for leakage and HFE that I got from Steve at smallbear, I think they were ETCO NPN Germanium 2N1306's. He suggested them when I told him about the direction I'm going with this design, as they have low leakage, and high HFE for NPN Ge transistors. But, the more I read about the rangemaster, it seems the HFE matters a lot. So I guess what I'm getting at now, is what is the role of HFE a circuit? If you change the transistor for a lower or higher HFE how will it affect the circuit? Does it affect the bias?

Mmmmmm. Good question.

The Rangemaster circuit is the so-called "stabilized bias" transistor circuit; collector and emitter resistors and voltage-divider bias network. The form of the circuit is called that because with those four resistors you can make a circuit which is remarkably consistent in DC bias over a very wide range of transistor parameters.  Yes, HFE does affect bias. It was years after transistors were invented before people understood what was happening with them, and how to design things which didn't need tweaked for every single different transistor, even of the same type number. The stabilized bias circuit uses DC feedback to stabilize things so that as long as the HFE is high enough, it will give fairly predictable DC bias performance.

Except for one item, this circuit would give predictable AC gain, too. If that 47uF emitter bypass cap was gone, the gain would be about 10K/3.9K for the pot turned up to the collector. That's because the feedback of the emitter voltage forces the gain to be that number, in a couple of ways. Putting the emitter bypass cap on there "shorts out" the AC feedback, and lets the transistor have it's open-loop gain back. The gain is much higher, but now is dependent on the HFE of the device as well as the collector current.

The commentary about wanting an HFE of 70-100 was aimed at getting a rangemaster circuit to sound like the prototypical ones sounded. In that gain range, the rangemaster sounds as expected. Bigger HFE (well, hfe, really; they're different) will give higher gains, more distortion and not the expected rangemaster sound. It'll still bias right, because the DC conditions of the stabilized bias circuit work with higher HFE too.

HFE and hfe play the role of putting limits on the maximum gains you could ever get out of a device if you had everything perfect. It is a fundamental concept of transistor design to never rely on an exact hfe to get your job done. Instead, you try to design circuits where you instead only rely on having *enough* gain, and then use feedback to burn off some of that gain in forcing the circuit not to depend on the exact gains. You trade maximum possible performance for predictability.

Another very fundamental concept in engineering is that whatever cannot be predicted and controlled must be made irrelevant somehow.

I swear every question leads to answers, that them bring up more questions it can be maddening.

If you keep this up, you're going to eventually get to a very good understanding of what you're doing. And you will have no one to blame but yourself. 

[rocket8810]

I understand what you mean about the hfe, which makes a ton of sense, since I read about high gain, low gain, medium gain transistors, etc. I asked one about hfe and its affects on a circuit and I got the response that essentially good circuit designs can work with any gain rating, but that it would change the bias. What you said makes me thing that if I replace a low gain transistor in a distortion pedal with a high gain transistor then I can alter the total distortion of the circuit. AHHH!!!! My mind is running on this now, so many questions coming to mind!!! I'd love to learn more about this, any good place to find out more about hfe and gain in circuits you could suggest?

If you keep this up, you're going to eventually get to a very good understanding of what you're doing. And you will have no one to blame but yourself. 

Thanks R.G. it's always good to get support, and hear words of encouragement, especially from someone who's been there. The constant questioning comes from being a scientist, and teacher. Before getting into pedal designing I could build and engineering almost anything, understanding the fundamentals of how circuits work has been a challenge. It's funny cause I my students never listen to what I have to say about learning, reaching out for help when you need it, and really working to solve problems rather than just look for an answer. Because if you don't know what your doing and why than, you can never apply it and do it on your own. It sucks being on the other side again.

But, I digress. I'm really glad to be part of the community, and have such a supportive environment, and I thank you guys so much so far. Hell, PRR and R.G. I swear if it wasn't for you guys I would not get this far, and probably would have given up. You guys, amongst many others on the forum always seem to have the answers, reasoning, and provide resources to help. Hopefully I'll be able to pass it on.

[PRR]

> Kind of off topic:
> more accurate in my estimation to say that physics is a series of demonstrations of how the properties of mathematical objects play out in the world of tangible objects.

If you actually care (or need a sleep-aid), read:

The Applicability of Mathematics as a Philosophical Problem, Mark Steiner.
http://www.amazon.com/The-Applicability-Mathematics-Philosophical-Problem/dp/0674009703
http://en.wikipedia.org/wiki/Mark_Steiner

I can't summarize it. But in-part, Mark argues that the "physics" we have IS math, not fundamental science. It is mostly selected for mathematical 'beauty', a human judgement, unlikely to be shared by raw matter/energy.

_I_ would suggest that Real Science on the very small/large/fast is VERY expensive/slow, while equation-diddles is cheap/fast. So it may be inevitable that wherever experimentalists go, they will find some "theorist" got there first. (Though perhaps with the right answer for a different problem.)

> It is possible that when God said "Let there be light..." it was really a set of....

Yes, and possible that we are getting a glimmer of His thinking. Steiner doesn't touch on that much. And the apparent goal of most physicists is not to reverse-engineer God's design, but to "understand" (and make predictions about) the reality we can observe. (Steiner does argue that there is a lot of goal-confusion in the field.)

[tubegeek]

The most advanced physics course I took before switching majors was a survey of "modern" (i.e., relativistic/quantum) physics given by the chairman of the department. He was a very good teacher, and he was also convinced that the "rightness" of the fit of math to physics was evidence of an overall organizing principle in the universe, whatever one might beleive it may be.

PRR - are you saying that Steiner would call that a sort of selection bias on the part of the observer?

Boy, it got deep in here awfully fast.....

[samhay]

My 2c worth:
It's relatively easy to do ugly numerical math with a computer these days, but you should still have an idea of what the answer should be before you hit enter - I think PRR touched on this.
Like others, I would suggest you give a circuit simulator a try - LTSpice is not a bad choice, but the falstad circuit simulator is nice and visual, if not a little unrealistic at times: http://www.falstad.com/circuit/

1. Think about what the circuit does.
2. Test it in a simulator.
3. Build it on a Breadboard.
4. Goto 1.

As far as the philosophy goes:
In addition to some past experiments in Social Zoology, I've been known to do a little theoretical biophysics. In a lot of respects, theoretical physics can be thought of as branch of applied math (a bit like engineering I guess). However, if the theory/predictions are not testable, then it is not science.

[rocket8810]

PRR a lot of the heavy ugly math theory can puts anyone to sleep. I swear its nearly as good a sleep aid as anything involving educational theory, which not only puts you to sleep but can knock you out for days. I want to touch on something R.G. Said about having a low pass filter that stops at least at the frequency we want. Is it better to go past? If so, how much? My concern is tht the more I've read about filters and frequencies that can cause problems. How is too low? (I've read it's 16Hz) How high is too high?

[samhay]

How is too low? (I've read it's 16Hz) How high is too high?

There is generally not much point going much beyond your hearing range unless you want to cause incontinence or frighten bats.

[R.G.]

I want to touch on something R.G. Said about having a low pass filter that stops at least at the frequency we want. Is it better to go past? If so, how much? My concern is tht the more I've read about filters and frequencies that can cause problems. How is too low? (I've read it's 16Hz) How high is too high?

Good question - again. Remember, it'll be your own fault. 

We talk about filters cutting off at some frequency. That's actually a polite fiction, useful for quick and dirty thinking about what's happening. As such, I really, really like it.    But it's important when using Q&D thinking to understand the underlying reality every time you use it. Filters never "cut off" at a frequency. The label "cut off frequency" or "turnover frequency" when applied to a filter actually means (by convention only) "the place where the transmitted signal power is only half of what it was far away from the filter frequency in the pass band."

So if we have a 100Hz high pass filter made with a single R and a single C [N.B.: These are referred to in the filter literature as "single time constant" or "single pole", from the complex-plane math describing them.] then at frequencies far higher than the "cutoff frequency", say 1000Hz, there is no appreciable loss of signal from there on up. In actuality, the amount of signal passed at the cutoff frequency is half the voltage, as the R and C have equal impedances there.

Notice that the phase has also shifted, too, as a capacitor passes current at 90 degrees leading the voltage across it. The R is always in phase, so the additive resultant is at 45 degrees for this single pole filter at the cutoff frequency.

If you graph the signal voltage out versus the signal voltage in, then out above 1000Hz, it's a flat line to infinity (or until something else affects it!) and it starts rolling off appreciably below 1000Hz. If the impedance of the cap is equal to the R at 100Hz, then it's 1/10th at 1000Hz, so the attenuation at 1000 is to 9/10 of the total input signal, and asymptotic to flat from there up. At 10Hz, the cap's impedance is 1/10 of the resistor, so the signal is attenuated to 0.1 of the incoming signal, and from there on down, it declines at -6db per octave, -20db per decade, on down in quest of DC. Between 10H and 1000Hz, the actual response is a smooth curve which intersects -6db at 100hz, flat out way beyond 1000hz, and -20db/decade way lower than 10Hz.

Engineers and scientists had to have some place to call the filter frequency, and they picked half-power, the changeover from resistor dominating to the cap dominating.

With all that as background, Paul's comment ought to make more sense. If you're picking a filter, you have some idea of how loud you want the signal at a given frequency compared to all other frequencies. So you pick a cutoff where it's really at changeover from flat to sloped, and see what you get. The real filter curve means that you get not exactly flat above the cutoff and not even close to cut off below the "cutoff" frequency. You get curves.

A prominent question that's now in your mind    is "what happens if I need it to cut off faster or be flatter near the cutoff frequency?" And the answer is - multi-pole filters. This question/answer is why I tossed in that aside about single-pole earlier. A single pole cutoff is pretty mild. The ENTIRE bass response through a Rangemaster circuit, for instance, is below the cutoff frequency of the input capacitor's filtering. So a single pole filter is kind of a tone shaper, not really a cutoff at all. Cutting off faster requires multi-poles, and worse, it needs all the multiple poles set up so they don't overlap and get in each other's way. And with multipole, you get ringing. The simplest two-pole filter is one capacitor and one inductor. Bango, two poles. But also ringing, and questions of how to damp the ringing, and whether some ringing is good either above or below the cutoff.

For faster, sharper cutoffs and flatter passbands, the math gets rapidly out of hand. You get flattest response filters ("Butterworth"), and a host of others which are optimized for some facet or other - elliptical filters, Cauer filters, Bessel filters, minimum phase filters, and 2 through N poles in each one.

Sorry, got off into the weeds again. The reason you might pick a cutoff that's not exactly where you want things to change is the non-ideal curved nature of the response curve. If you HAVE to have little loss at 32Hz, you probably should put your bass cutoff down at 3.2Hz, where you only lose 10% of your signal to the lowpass. If that makes things muddy, you have a conflict: you can't get full response to 32 and not also pass more of the lower stuff. Maybe you could do with a little less 32, but also less mud. And at the high end, is 8kHz "clear" enough when it's passed at 50%? Or do you have to have 90% of the 8kHz content, knowing that you're going to let through stuff up to 80kHz to get your 8K?

Then there's how you'd pick that. That requires not only engineering understanding, but also taste and aesthetics. Then it gets tough.

[PRR]

> How is too low? ... How high is too high?

Well, "it depends", no?

How big is a house? Is 2 rooms too small? Is 90 rooms too big? Evidently both extremes are "reasonable" to someone.

How big is a guitar speaker? Some guys play one 6-inch, others run a eight 10-inch stack.

Speaker size is a lot to do with bass-cut. There's no point in electronic bass to 1Hz when a six-inch gets flubby below 100Hz. OTOH eight 10s can be authoritative below 50Hz. Even "too much": Marshall often slopes-off some bass so the guitar scream does not get smothered in mud.

Nowadays it is perfectly possible to build an audio system with no bass cut-off, response to DC. The immediate problem is that 1st-stage DC errors tend to be not-small compared to signal levels. e-Guitar delivers 200mV audio but a TL072 can have 5mV DC error. Amplify this to 20V at the speaker, that's a half-Volt of DC at the speaker. Won't kill it, but uses-up a good part of the available cone motion, adds heat to power-amp and voicecoil. And is useless: speakers can't deliver "DC pressure" (unless in a sealed room), and no music uses DC pressure changes (equivalent to barometric changes).

And some sources have strong subsonics. Studios with air blowers may be well-muffled above 50Hz, but fan rumble rises at lower frequency, good bass filters are HUGE, it is not unusual to have 90dB SPL below 20hz. Record-players (still around!) tend to have a 1.8Hz thump plus various bearing grumbles. All amplifiers have 1/f noise, apparently rising to infinity at zero frequency. I have seen 1/f noise saturate a phono system (cause power-amp DC protection relay to cut-out).

Practical speakers are flat to 100Hz-50Hz. You can't hardly hear a 1dB droop. So it is reasonable to design a Reproduction System for less than 1dB at 50Hz, or (for a single pole) -3dB at 25Hz.

That's a "DC" system with ONE pole bass cut. Typical systems are many stages with coupling caps at every stage. Easily six or ten 1-pole filters in cascade. If each is -1dB at 50Hz, you wind up at -10dB 50Hz which IS a big drop. In simple systems, you pick one or two bass-cuts near the bottom of your audio band, and set the others a few octaves or more below that.

> filters and frequencies that can cause problems.

Everything filters. Both guitar pickups and loudspeakers use overlapping high and low pass effects to get some semblance of "flat". Not quite flat, we may filter-away some error. And dead-flat is not the goal in music Creation-- we want final spectra which is "pleasing". Strings are heavy, string vibrations are mellow. We use small thin shells (violin, guitar) or velocity pickups (e-guitar) to bring up the overtones. Harmonics above the 7th or so are un-musical, we use bridges or speakers that cut-off extreme treble. (At 4KHz-8KHz, mechanical filters can give much sharper cutoffs than any few R-C networks; look at the high end of a guitar-speaker's response compared to a 3-pole Butterworth, or the many-RC filter on some speaker simulators.)