"Basic transistor amplifier theory gives you the answer. If there's no emitter bypass capacitor, the gain of a correctly biased single transistor stage is determined by the ratio of the collector resistor to the emitter resistor - it's collector resistance divided by the emitter resistance. You can therefore see that the gain is increased by using a bigger collector resistor or, conversely, a smaller emitter resistor."
Chris (last name withheld), Electronics Engineer.
It was this quote that gave me the idea to create a standard for measuring the gain of Big Muffs so people can more accurately judge which Big Muff is for them.The gain factor theory I have cobbled together for Big Muffs is a guide only, it's not 100% infallible as other factors determine gain aside from resistors and it isn't intended to be the final word on Big Muff gain.However, It is intended to give the user a "pretty good idea" of how his/her Big Muff stacks up to other versions as far as gain/distortion is concerned. I have tested this method on various Big Muffs and it is a quite reliable way of determining the gain of any one particular Big Muff compared to any other particular Big Muff to determine which is higher gain than the other. I took various Big muffs (10 in total) which I knew were low gain, medium gain, and high gain and calculated the gain factor of them. The lowest gain Big Muff with least distortion (like a heavy overdrive-semi distortion) had the lowest gain factor, the highest gain and most distorted Big Muff had the highest gain factor. If you are wanting to determine the mid-scoop of the Big Muff I would refer you to the "Duncan Tone-Stack Calculator" for very accurate figures as its a very useful tool for seeing the amount of mid-scoop any particular Big Muff has. There is also a lot of misinformation is this field as well regarding which Big Muff is more scooped etc. The reason I have created this ranking system for Big Muffs is because I often read on musicians forums something like the following: "This ramshead muff is heaps lower gain than than a NYC RI Big Muff" or this Green Sovtek Big Muff is far higher gain than the NYC RI Big Muff". However, once I have seen an internal photo of the circuit and the values of the components used or I have a schematic for that exact Big Muff or I own an identical one myself I can usually tell if this is or is not the case and in fact it is often actually a reversal of what the individual is claiming. Basically, I have put together this system to counter Big Muff misinformation which the www is full of and at the same time educate Big Muff fans.
The gain factor is achieved by calculating Q1,Q2 and Q3 only as Q4 is negligible and not worth the calculation as it plays such a small factor in the calculation itself and this stage is only in the Big Muff to recover volume which is lost due to the passive tone-stack.
First we add up the total Ohms of the collector resistor, then divide it by the total Ohms of the emitter resistor, for example: A collector resistor with the value of 15k would be 15,000 Ohms.If the emitter resistor is 100 Ohms we divide 15,000 by 100 which gives us 150. This is the gain factor for the first stage (Q1). We then repeat the process for stages 2 and 3 using the values we see in each stage and once we have done so we multiply these three numbers together, the result is the gain factor of your Big Muff! For example, If all three (Q1-Q3) stages have a gain factor of 150, the total gain factor for this particular pedal is 450, a high gain Big Muff. If the total number reached is only 92 (Typical Sovtek Big Muffs), its a fairly low/medium gain Big Muff...relative only to the gain available in the Big Muff circuit. For Big Muffs with variation in collector/emitter resistor values the calculation is still valid but it can be less indicative of the amount of gain/distortion your Big Muff is putting out. The ranking system is not perfect and is not fool proof but it does give people an idea instead of buying blind like a lot of people do today. With internet sales taking up such a large proportion of Big Muff purchases (especially second hand) having the opportunity to actually test the pedal in question before hand is not always possible.
Note: 1k (Kilohms) = 1,000R (Ohms).
Examples from actual Big Muff pedals: (Q1, Q2 &Q3 single stage calculation only, x 3 for total)
12k / 390R = gain factor of 30.7. (Typical Sovtek Big Muff gain stage)
10k / 120R = gain factor of 83. (Typical 2008 NYC RI gain stage)
15k / 100R = gain factor of 150. (V6 3034 Big Muff gain stage)
12k / 150R = gain factor of 80. (One example of a V2 ramshead Big Muff gain stage)
High Gain mods: (Q1,Q2 & Q3 single stage calculation only, x 3 for total)
15k / 75R = gain factor of 200. (High)
15k / 50R = gain factor of 300. (Very High)
15k / 25R = gain factor of 600. (Extremely High)
10k / 0R = gain factor of 10,000 (Insanely High and a common mod believe it or not. You can just jumper these emitter resistors.)
Medium/Low Gain mods: (Q1,Q2 & Q3 single stage calculation only, x 3 for total)
12K / 390R = gain factor of 30.7.
10k / 390R = gain factor of 25.6.
8.2k / 390R = gain factor of 21.
I chose to keep the collector resistors at or below 15k and lower the emitter resistors more as this sounds best in my experience.
Somethings to note: The difference between the typical Sovtek Big Muff total gain factor (92.1) and a 2008 NYC RI Big Muff total gain factor (250) is just under three times more. This does not equate to one actually hearing three times as much gain, yes you will hear an increase in gain/distortion but it wont be extreme in this comparison...its very noticeable but its not what you would likely expect, I would call it a subtle yet very noticeable difference...if that makes sense :p. The difference between a Big Muff with a gain factor of 92 and a Big Muff with a gain factor of 450 is only about 50% more gain at the upper end of the scale, it may be slightly less than this so you can see that you have plenty of room to experiment with this as big resistor changes dont equate to absurd gain increases. Anyways, in the case of Big Muff modification to increase/decrease gain-distortion the results are very audible and very pleasing. An increase/decrease in volume will also accompany the modification, which way depends on which way you go. If you make your Big Muff higher gain the volume will increase slightly, its very minor and you likely wont even notice it with most modifications.
Another thing to note is the hFE (gain) of the transistors used. This will always be a variable in this system but it is insignificant (to a certain extent) in my opinion. I have tested Sovtek Big Muffs with transistor gain (hFE) of 750+ in all four stages and American Big Muffs with a transistor gain (hFE) of 450 and because of the collector and emmiter resistor values used in the American Big Muff, the one with the lower gain transistors, is actually a higher gain pedal than the Sovtek pedal.
So, a Big Muff that used 2N3904 transistors with an average hFE of 200 used in conjunction with the right resistor values can be a higher gain pedal than a Big Muff that uses 2N5089 transistors with a hFE of over 600 if the appropriate value collector and emitter resistors are chosen.
The Way Huge Swollen Pickle is an excellent example of this as it uses a quad transistor array with a similar hFE as the 2N3904 yet is still high gain with a gain factor of around 450.
That is not to say transistor hFE and transistor type wont change the sound of the Big Muff as it will, you will achieve varying results from various transistors used. Some good ones are (NPN):2N5088 (An Electro-Harmonix favorite), 2N5089, 2N3904, 2N2222, 2N5133, 2N550B, 2N550C, 2N3565, BC108B, BC108C, BC109B, BC109C, MPSA18. / (PNP) 2N3906, 2N5087 and just about any other medium to high gain silicon bi-polar transistor works well.
Using the 2000 NYC RI Big Muff with a gain factor of 151, which almost everyone knows the sound of, as a standard for gain measurement you should be able to make a more educated decision on which Big Muff is best for you using this formula, as far as gain is concerned anyways.
The current 2008 NYC RI Big Muff has a gain factor of 250 and the Big Muff With Tone Wicker has a similar gain factor.
If you want more gain than the RI Big Muffs you should look into modifying your Big Muff so it has a gain factor of 450 for starters and then go from there. A gain factor of 450 (high but far far from excessive.) is a nice sounding Big Muff with a nice amount of distortion, The 1981 3034 Big Muff I have has a gain factor of 450 and is by far one of my personal favorites. When modifying your Big Muff it is recommended that you increase by increments of between 5k - 10k for collector resistors or if decreasing the emitter resistors, by increments of 100 Ohms so as to not to overdo it and potentially miss the sound you may have liked and create one you hate."Let's consider the two clipping stages. Imagine that the first stage has a 15k collector resistor, and a 220R emitter resistor. We've got a nominal stage gain of X 68~. Let's say that the next stage has 10k collector and 220R emitter - gain of X 45~.
Now let's apply some audio. Let's use a tone of 1 kHz (a good enough test frequency for our thought experiment) with an amplitude of 50 mV p-p (which isn't unreasonable from a guitar). The first stage is going to try to multiply that 50mV to 3.4 V p-p. However, the diodes are going to be conducting hard part way into each cycle, when they see 0.65 V across them, so the actual output will be very distorted, and much smaller!
OK. Let's say that the output of the first stage is 0.7V p-p. The second stage is going to try to achieve 31.5 V p-p, which again isn't going to happen because the diodes will clamp the signal, and because the transistor only has a (nominally) 9 Volt supply to play with! Again, you're going to get really gross distortion with lots of harmonics (which is actually what we want! :D )"
Chris (last name withheld), Electronics Engineer.
Another factor that can make this gain factor theory go out of wack a bit is diodes! Depending on which diodes any one Big Muff has in it will also determine to a certain extent the amount of gain/distortion it puts out. I am assuming, when you measure the gain factor of a big muff, that it is a stock big muff with silicon diodes in it and not red LED's or Germanium diodes for example. The reson for this is because different diodes clip harder than others.
Germanium diodes clip softly, silicon harder and red LED's clip even harder. The harder the diodes clip the more gain/distortion is going to be generated so bare this fact in mind when determining gain factors. For examples of the way certain diodes clip the waveform look in the "schematics and modifications" section of this website for an example pic and also refer to the "Diode clipping in the Big Muff" section of this website.
So, now you know about choosing the gain of your Big Muff you can experiment with it and once you're happy you can concentrate on other parts of the circuit like the Input/Output, clipping, high frequency and coupling caps with a little modification, can drastically change the sound of your Big Muff for the better. (or worse :p )
I will add articles on these factors and others at a later date.