Orange Squeezer Schematic Clarification

Started by blacklightruckus, June 04, 2012, 08:52:54 PM

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blacklightruckus

I was hoping for some clarification regarding transistor 1 in this diagram: http://www.tonepad.com/getFile.asp?id=11

Is this statement correct?:

In this case there is a 2k4 resistor connecting to the transistor's base, collector and the 4u7 cap.

If so, my question is, where does the emitter connect to?

hannibal827

The transistors in this circuit are JFETs, not bipolars, so they don't have emitters, bases, or collectors per se.
Instead the three pins are: drain/source/gate.

The junction you're referring to is as follows: one lead of that 2k4 resistor connects to the gate of one JFET [Q2 in the more recent layout], the source of the other [Q1 of the more recent layout], the positive end of the 4u7 electrolytic cap, and lugs 1 and 2 of the "sustain" pot.  Transistor 1 [I'm assuming you mean Q1, although in the layout you're linking to they are not numbered] has its gate connected to the junction of the two 470k resistors, and its drain connected to the junction of an 82k resistor, a 2n2 capacitor, and a 47n capacitor.  Transistor 2 has its drain connected to +9v and its source connected to the other lead of that 2k4 resistor.

OT: why not use the more recent layout, with "sustain" as a trimpot?  It really is more like a bias trimmer than an actual "sustain" control as seen on other compressors.
Pedals built: Pulsar; Uglyface; Slow Gear; Tri-Vibe; Tremulus Lune; Blues Driver; Fender Pro Vibrato; Nyquist Aliaser; Ultra Flanger; Clone Theory; Ibanez FL-301; Echo Base; Electric Mistress (Deluxe); Boss CE-2; Gristleizer; Maestro Filter Sample/Hold.

blacklightruckus

Thanks hannibal, I'm with you so far!

The component I'm looking at is Q2, and the up arrow goes to +9v. That leaves me with two last questions:

1. Is an up arrow like that, a standard symbol for return to +?
2. Having the "sustain" knob as an internal trim pot is ideal, because the knob shouldn't ever have to be adjusted? If so, is this the diagram you're going by? http://www.tonepad.com/getFile.asp?id=88

hannibal827

Quote from: blacklightruckus on June 05, 2012, 08:16:38 AM
1. Is an up arrow like that, a standard symbol for return to +?

Typically, yes, unless otherwise indicated.

Quote from: blacklightruckus on June 05, 2012, 08:16:38 AM
2. Having the "sustain" knob as an internal trim pot is ideal, because the knob shouldn't ever have to be adjusted?

You should adjust the trimpot to get a sound you like, yes, and then close up the box and leave it alone.  If you built it as an external pot, you would, if I remember correctly, find that the circuit wouldn't work properly over the entire range of the pot's rotation.  That's why the original layout refers to it as a "bias" pot.

Quote from: blacklightruckus on June 05, 2012, 08:16:38 AM
If so, is this the diagram you're going by? http://www.tonepad.com/getFile.asp?id=88

Yep, that's the one.  Good luck!
Pedals built: Pulsar; Uglyface; Slow Gear; Tri-Vibe; Tremulus Lune; Blues Driver; Fender Pro Vibrato; Nyquist Aliaser; Ultra Flanger; Clone Theory; Ibanez FL-301; Echo Base; Electric Mistress (Deluxe); Boss CE-2; Gristleizer; Maestro Filter Sample/Hold.

midwayfair

Quote from: hannibal827 on June 05, 2012, 08:38:22 AMYou should adjust the trimpot to get a sound you like, yes, and then close up the box and leave it alone.  If you built it as an external pot, you would, if I remember correctly, find that the circuit wouldn't work properly over the entire range of the pot's rotation.  That's why the original layout refers to it as a "bias" pot.

Theo Hartman's mod fixes that problem and would allow you to have some fine control over the squeeze without dead spots or compressionless settings.

I did one Squeezer with an external bias knob and really wish I hadn't. But now I just prefer having external volume and not fiddling. Trim pots are cheaper than pots and knobs, too. :)
My band, Midway Fair: www.midwayfair.org. Myself's music and things I make: www.jonpattonmusic.com. DIY pedal demos: www.youtube.com/jonspatton. PCBs of my Bearhug Compressor and Cardinal Harmonic Tremolo are available from http://www.1776effects.com!

hannibal827

Midwayfair, thanks for that info.  I wasn't aware of that mod.

I did a quick search, and while I haven't found a schematic yet, I did find this thread: http://www.diystompboxes.com/smfforum/index.php?topic=80392.0

The jist of it seems to be that the Hartman mod allows you to back off the amount of compression.  Personally this struck me as odd--of the three compressors I've built [the other two being the DOD 280 and the Ross], the Orange Squeezer is by far the most subtle and transparent.  It sounds fine, but I can't imagine wanting less compression than this circuit delivers.  But to each his own, I suppose.

I built my Orange Squeezer with the internal bias trimpot, haven't looked back, and have no regrets.
Pedals built: Pulsar; Uglyface; Slow Gear; Tri-Vibe; Tremulus Lune; Blues Driver; Fender Pro Vibrato; Nyquist Aliaser; Ultra Flanger; Clone Theory; Ibanez FL-301; Echo Base; Electric Mistress (Deluxe); Boss CE-2; Gristleizer; Maestro Filter Sample/Hold.

blacklightruckus

#6
So in my hunt for good parts for this build, I can't seem to find any 1n100, 1n34a, or 2n5133. I understand that SE4010 is a similar part with higher gain. Will this work for the squeezer?

Do you guys have any good recommendations for this part? Would one of the NTE replacements on this page do the trick without degrading the quality of the build? http://www.mouser.com/Search/Refine.aspx?Keyword=germanium+diode

hannibal827

Quote from: blacklightruckus on June 05, 2012, 12:04:08 PM
So in my hunt for good parts for this build, I can't seem to find any 1n100, 1n34a, or 2n5133. I understand that SE4010 is a similar part with higher gain. Will this work for the squeezer?

I'll get to the diodes in a sec.  2N5133 and SE4010 are inappropriate transistors for this circuit.  They are NPN bipolar junction transistors, and the circuit calls for JFETs to work properly.  2N5457 is the part indicated on the schematic, but MPF102 or J201 might also work.

Quote from: blacklightruckus on June 05, 2012, 12:04:08 PM
Do you guys have any good recommendations for this part?

You can get 1N34A diodes pretty cheaply on eBay, but Small Bear Electronics also has workalikes [listed as NOS Germanium], and they are a good supplier to support. https://www.smallbearelec.com/home.html  I don't know if another type of diode works in that spot.  Small Bear also has 2N5457s and other JFETs, by the way. 

Quote from: blacklightruckus on June 05, 2012, 12:04:08 PM
Would one of the NTE replacements on this page do the trick without degrading the quality of the build? http://www.mouser.com/Search/Refine.aspx?Keyword=germanium+diode

I can't speak for the quality of the NTE replacements, but they are almost always overpriced compared to the real thing, which is almost always out there.
Pedals built: Pulsar; Uglyface; Slow Gear; Tri-Vibe; Tremulus Lune; Blues Driver; Fender Pro Vibrato; Nyquist Aliaser; Ultra Flanger; Clone Theory; Ibanez FL-301; Echo Base; Electric Mistress (Deluxe); Boss CE-2; Gristleizer; Maestro Filter Sample/Hold.

midwayfair

Quote from: hannibal827 on June 05, 2012, 12:49:13 PM
Quote from: blacklightruckus on June 05, 2012, 12:04:08 PM
So in my hunt for good parts for this build, I can't seem to find any 1n100, 1n34a, or 2n5133. I understand that SE4010 is a similar part with higher gain. Will this work for the squeezer?

I'll get to the diodes in a sec.  2N5133 and SE4010 are inappropriate transistors for this circuit.  They are NPN bipolar junction transistors, and the circuit calls for JFETs to work properly.  2N5457 is the part indicated on the schematic, but MPF102 or J201 might also work.

J201 sounds bad in this pedal ... and most circuits. :) (Seriously, I am not a fan of that FET.) It has higher gain than the 2N5457, and this causes some weird biasing problems and, in my experience at least, an undue amount of thump. I like a little tiny bit of thump, but the 201s had too much in every bias setting.

Quote from: hannibal827 on June 05, 2012, 12:49:13 PM
Quote from: blacklightruckus on June 05, 2012, 12:04:08 PM
Do you guys have any good recommendations for this part?

You can get 1N34A diodes pretty cheaply on eBay, but Small Bear Electronics also has workalikes [listed as NOS Germanium], and they are a good supplier to support. https://www.smallbearelec.com/home.html  I don't know if another type of diode works in that spot.  Small Bear also has 2N5457s and other JFETs, by the way.

Any germanium diode will work, and there is absolutely nothing special about 1N100 except that they're unobtanium. You want something with a Fv clipping threshold of .3v or lower, which is every Ge diode out there. I've used 1n270 with great success more than once. They tend to have a very slightly lower forward voltage than a 1n34a, so they may very slightly increase the amount of compression you get. It's not in the audio path, but I also swear that I get more highs with it, which may be nothing more than biasing, but who knows, it could simply be that it's compressing all frequencies a little more evenly.

There are two places I get my Ge diodes: Smallbear and Scott's Electronics (Angelfire.com). Scott's has a good deal on packs of 25 Ge diodes (not the 1N270s, but his price is still good), which is good if you're like me and you stick Ge in everything they work in. :) Otherwise, for small quantities, order them from Smallbear with your other parts. Pedal Parts Plus has 1n34as, too, but the price is a little higher.
My band, Midway Fair: www.midwayfair.org. Myself's music and things I make: www.jonpattonmusic.com. DIY pedal demos: www.youtube.com/jonspatton. PCBs of my Bearhug Compressor and Cardinal Harmonic Tremolo are available from http://www.1776effects.com!

R O Tiree

#9
Wall of text coming...

First off, Dan Armstrong was pretty much a genius, working all this out from scratch - no computers to run PSPICE simulations in those heady days, just a slide-rule, pencil, paper and a whole bunch of quite complex equations.  Once you understand how this circuit works, though, you get a light-bulb moment... it is an elegant solution.

The 2 FETs are working in different modes, in this circuit.  Referring to the TonePad layout, Q2 is just using +9V, 2.4k and the 10k trimpot to GND to maintain a constant voltage at its Gate, which cunningly also holds Q1's Source rock-steady at the same exact voltage.  Don't worry about Q2 from here on in - it's done its job and it's nothing to do with the signal chain.  OK, on to Q1... FETs can also act as a voltage-controlled variable resistor.  You see them all the time in Boss and Ibanez switching systems, but in those systems, they're alternating between fully on and fully off to route the various processed and unprocessed signals around the place.  This circuit uses them in a more subtle fashion.  It might be worth a few lines on how they work:  In an N-channel FET, you have a slab of N-type semiconductor connected to Drain and Source.  A current will therefore pass quite readily through it.  Tack a blob of P-type semiconductor to the side of it and call it a "Gate" and then vary the voltage at the Gate.  What we're looking for, here, is the voltage between Gate and Source (called Vgs).  If you lower the voltage at the Gate, you create a diode between there and the Source that is reverse-biased.  Refer to any text-book on the subject and you'll understand that a depletion layer develops around that P-N junction.  This effectively narrows the area in the slab of N-type through which current can pass.  That same text-book will also tell you that resistance of any material depends (among other factors) upon its cross-sectional area.  Ta-daaaaaah!  Voltage controlled resistor!  Raise the voltage at the Gate to match Vs and you have max throughput of current, lower it sufficiently and you end up with a HUUUUGE resistance.  Somewhere between those extremes and you can regulate it, kind of like squeezing a garden hose... the more you bear down on the hose, the more you restrict the flow.  (Reverse this explanation for a P-channel JFET.)

What we're trying to do with that trim-pot is to get that "Goldilocks" Vgs that is juuuuuuuust cutting off the flow when you have extremely small signals coming in to the pedal.  We'll come back to Q1 again in a minute...

OK, now to the op-amp.  Its gain is controlled by the 10k and 220k resistors, giving a gain of just over 20, but there are lots of deliberate losses elsewhere in this circuit, giving a gain of about 12 which is quite tame for a compressor, really.  Perhaps one reason why this circuit is so highly regarded... it doesn't bully the sound at all.  So, how is this circuit varying the gain, then, because the gain of that op-amp is fixed?  Here goes... At the output of the op-amp is that series of 1.5k, Ge diode and 100k tacked in parallel with the 4.7µF cap. There's then a wire running from the top of the cap via the 470k resistor to Q1 Gate.  With very small signals coming into the pedal, the voltage in that wire just drops and drops, the charge in the 4.7µF cap dribbling away to GND through the 100k resistor, eventually reaching just about 0V.  The resistance of Q1 is pretty high, therefore.  Hit a big chord and it gets amplified 20 times... suddenly, there's a voltage spike at the output and that little Ge diode starts to conduct every time the output exceeds +0.3V with respect to the top of the cap.  The current has 2 ways to go... through the 100k resistor or fill up the cap?  Not a difficult decision - the cap is empty, so that's where the charge goes, so its stored voltage rises.  As it does so, the voltage at Q1 Gate rises, so the resistance between Q1 Drain and Source reduces.  Current can now flow and it bleeds a little bit of the input signal away to ground (via the 4.7µF cap underneath Q1 and Q2).  The percentage that travels via the 0.047µF cap and into the op-amp is still amplified 20+ times, it's just that there's not as much percentage getting there as before.  As the input signal from your guitar drops away, that diode stops pumping up the cap and the voltage in it dribbles away again via the 100k resistor.  The voltage at Q1 Gate drops, gradually restricting the bleed-away of input signal and the percentage of signal going to the op-amp increases.  Thus, the chord is sustained for longer than it should be.

The only bit I haven't talked about is the other 470k and 2.2nF cap from Q1 Drain to Gate.  They are simply there to provide 1/2 the Drain signal to the Gate, which stabilises and linearises the FET's behaviour.  The cap strips out the DC voltage and the 2 x 470k resistors act as a voltage divider.  They're quite large, so they don't allow any pumping up of the 4.7µF cap... there's not much current from a 100mV signal after travelling through a 1M total resistance and, in any case, it's AC, not DC!

So, in summary, most compressors control the gain of an op-amp.  This one doesn't - the op-amp is at a fixed gain figure and the trick the FET does is to alter the proportions of input signal that get bled away to GND or go through the op-amp.  The FET has no direct influence on the sound at all.  So, why do different FETs behave differently?  Remember that Vgs I mentioned?  Different types of FET have different Vgs figures (in a pretty wide band, actually, because they're much harder to make consistently than other transistors).  They also have different ON resistances and different resistance curves.  If anyone knows of a cast-iron substitute for a 2N5457...?  I'm playing with this circuit at the moment, so I'd be interested in others' experiences.

OK, what about REALLY big signals?  Well that diode pumps and pumps at that cap, raising the voltage, so Q1 bleeds away an even bigger percentage of the input signal to GND, leaving even less to get through the op-amp.  There will be an input signal level where the output is actually less than the input.  It's not a limiter (which puts a hard limit on output level), it's a compressor.

So, that 10k trimpot is not a compression control, really - it's purely there to bias Q1's Source at that "Goldilocks" voltage.  Mark Hammer published a mod some years ago to alter the gain of the op-amp... replace the 10k resistor with a 10k pot in series with a 6.8k resistor.  Wind the pot to 0 ohms and you get much more amplification in the op-amp than in the basic circuit (6.8k outside, 220k inside = gain of 32+1 = 33!! (non-inverting, remember) so, about 20 after losses...).  Wind it up to 10k and you'll get less (16.8k outside, 220k inside = gain of 14. About 8 after losses).  That's a much more elegant way to control things than deliberately mis-biasing Q1.

I hope (a) I got this all correct and (b) that it helps.
...you fritter and waste the hours in an off-hand way...

John Lyons

Wow...I realize I'm late to this thread but...no reply to the info given above.
Jeez folks...
Thanks R O!
Basic Audio Pedals
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Perrow

I'm tired and the painkiller hasn't really done away with the headache, but at some point I've got to read through that wall of text. I've got a Squeezer on a veroboard that needs me to understand this circuit.
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Kesh

Just wanted to hijack this thread with my own question about the OS. I built one but never boxed it owing to a noise issue that wasn't the usual comp noise. Basically a hiss to a gurgling was present over the usable portion of the bias preset. I assumed it was some oscillation that the bias control was tuning and a well placed cap might kill it? Any ideas?

.Mike

When you say "usable portion of the bias preset," do you mean the part where sound came out, or the insanely small part of the trimpot that allows the OS to actually function like a compressor (where crunching/scratching noises are heard while you adjust it)? That's the part of the trimpot adjustment that offers compression. Above the crunchy scratchy portion, the OS is a booster, and below the crunchy scratchy portion, the OS is a muter.

Others disagree with my assessment of the bias adjustment, but my own tests indicate that a lot of OSes are being used as boosters-- especially the ones with the external bias adjustment nonsense.

Maybe, if R O knows the details of the bias adjustment, he can maybe explain it with a little more depth. :)

Mike
If you're not doing it for yourself, it's not DIY. ;)

My effects site: Just one more build... | My website: America's Debate.

hannibal827

Pedals built: Pulsar; Uglyface; Slow Gear; Tri-Vibe; Tremulus Lune; Blues Driver; Fender Pro Vibrato; Nyquist Aliaser; Ultra Flanger; Clone Theory; Ibanez FL-301; Echo Base; Electric Mistress (Deluxe); Boss CE-2; Gristleizer; Maestro Filter Sample/Hold.

Kesh

Quote from: .Mike on October 04, 2012, 03:45:29 PM
When you say "usable portion of the bias preset," do you mean the part where sound came out, or the insanely small part of the trimpot that allows the OS to actually function like a compressor (where crunching/scratching noises are heard while you adjust it)? That's the part of the trimpot adjustment that offers compression. Above the crunchy scratchy portion, the OS is a booster, and below the crunchy scratchy portion, the OS is a muter.

Others disagree with my assessment of the bias adjustment, but my own tests indicate that a lot of OSes are being used as boosters-- especially the ones with the external bias adjustment nonsense.

Maybe, if R O knows the details of the bias adjustment, he can maybe explain it with a little more depth. :)

Mike
I mean that small portion where compression occurs. The crunching's gain change was a great way to hear the compression. But I'd have rather heard it in the signal. Is this noise just a feature of OSes, or can it be reduced?

R O Tiree

#16
Quote from: .Mike on October 04, 2012, 03:45:29 PM
When you say "usable portion of the bias preset," do you mean the part where sound came out, or the insanely small part of the trimpot that allows the OS to actually function like a compressor (where crunching/scratching noises are heard while you adjust it)? That's the part of the trimpot adjustment that offers compression. Above the crunchy scratchy portion, the OS is a booster, and below the crunchy scratchy portion, the OS is a muter.

Others disagree with my assessment of the bias adjustment, but my own tests indicate that a lot of OSes are being used as boosters-- especially the ones with the external bias adjustment nonsense.

Maybe, if R O knows the details of the bias adjustment, he can maybe explain it with a little more depth. :)

Mike

OK, here's what I've observed...

EDIT... I have just realised I got Q1 and Q2 reversed when I wrote this post.  I have now amended it to "agree" with my original post at Reply #9 and the TonePad layout that we were referenced to.  Sorry, everyone :-[

Q1G is at as near 0V with 0V input signal as makes no difference - a couple of µV, perhaps.  Can you measure that?  No.  So, if Q2G is set too low, Q1 VGS isn't enough to get it to completely "switch off", so Q1 leaks like a seive and your compression is pants.  This is because you cannot get Q1G any lower than 0V so, if Q1S (=Q2G voltage) is not sufficiently high with respect to its gate, it's going to leak some/lots of your signal to ground, depending on how badly you've biased it.

Going the other side of the "Goldilocks" bias point, I get the same crunching/scratching noises that .Mike has described when feeding it with a test signal.  They seem to be rhythmic in nature, cycling in and out.  I haven't looked that deeply into where it's coming from and perhaps I ought to, but bear with me...

The way I bias mine is to measure Q1's VGSoff in a test circuit.  You know that FET matching circuit at geofex for hitting the sweet spot with P90s?  It turns out (obvious when you think about it) that that circuit acts as a comparator for when RDS=10k.  If you substitute the 10k resistor for a 2M2, for example, you're getting to well within a µV or so of VGSoff (check out who's just discovered the subscript function in here  :icon_biggrin:).  Again, can you measure that?  Clearly not... you'll be lucky to get within 1 mV with most DMMs.  Can you set it within 1mV with the trimpot?  You'll be trying for a long while, and it will drift very slightly with temperature changes anyway.  So, adjust the trimpot so Q2G is at Q1's measured VGSoff within a few mV.  Once it's in the ball-park, tweak until that really annoying noise disappears and then give it the tiniest of nudges towards the "leaky" side and you're golden.
...you fritter and waste the hours in an off-hand way...

PRR

> mis-biasing Q1

The intent is:

FET turn-off voltage varies (as you say) with temperature. Getting a turned-off reference voltage from an FET will be more consistent across temperature. (True, FETs don't wander that much across the temp-range that musicians are comfortable in; but tempco cancellation can get to be a habit.)

Battery voltage sags. A resistor divider will give a varying reference, although the FET itself does not see batt voltage and does not change as battery ages. (This may be less important in a day of wall-power pedalboards.)

And I would say that SPICE is not helpful in basic design of most audio, especially limiters. You get mired in minute details and miss elegant approaches.

I would even deny the usefulness of a slide-rule. I have one here and I'm not afraid to use it; but 9V/2K7 is "about 3mA" for most practical purpose, and it is very unhelpful for 100K*10uFd because a slide-rule does not keep track of the decimal point. On the slide-rule, 100K*10uFd looks like "1*1" and you can solve that on sight. Even for 120K*22uFd, you ought to be able to see this is about twenty times a hundred, and the 32% error is in a factor (ear response) which can't be precisely specified and a "right" answer will have to be found experimentally.
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R O Tiree

All who have read my Reply #16 and thought, "What??", please see my edit... Wotamuppet.  Sorry.

Thanks, Paul.  The point of that wall of text was to try to assist blacklightruckus in understanding the circuit and why breaking out the Q2 trimpot onto the front face of the box was not going to prove terribly useful for a significant proportion of the pot's travel.  Also, that the circuit needs to be juuuust at the "Goldilocks" point for max efficacy at what it tries to achieve.

As I was writing the reply immediately before yours, where I was talking about tempco, I thought to myself about a dying battery and thought, "Tweaking towards the leaky side helps that as well."  Then I  wondered if something like an 8.2V Zener would be useful in providing a pretty stable voltage reference to Q2D... then I thought, "Naaaaah.  It's a current-source.  It's going to be stable down to stupidly low voltages... Disregard that idea."

As to SPICE, you know all this, I'm positive, and will have heard it all before, perhaps... but here's my take on it.  Sure a back-of-fag-packet calculation will get you in the ball-park, especially when you consider the often wide variability of components, and 99% of the time it's all you need... BTW, "fag" here in UK is a cigarette, not a ... never mind, moving on... But SPICE is really useful for me when I spot a circuit fragment and think, "Qué?"  I've had a lot of smack-forehead moments when watching circuits on screen that would have taken many hours of tedious mucking about with bread-boarding.  And bread-boarding can be very finicky, legs of components shorting out when they shouldn't, not making a solid connection in the holes, probing a voltage and ending up touching some other component leg and getting odd results left, right and centre.  Going straight to PCB gets expensive if there's a mistake in the design.  SPICE lets me know if a small change in a particular component value leads to a large change elsewhere, so I know I'm going to need some means of adjusting it at build time.  It does it with varying degrees of accuracy, for sure (your comment a while ago about simulation is largely useless unless you know roughly what should happen - I'm paraphrasing, but that was the gist of it) but I find I can very quickly get to the heart of a problem area to decide what's important and what isn't.  If I can't see why a designer chose method A over method B, very often a quick SPICE anim proves the point as soon as I hit "Run"... or not, and I then have to wonder whether building it would prove it one way or the other.  Sometimes I don't actually want to build the whole circuit at all - I just want to find out what's going on in there, as I might find the concept behind a particular fragment useful elsewhere.  I hear you loud and clear when it comes to taking the results with a small pinch of salt, but my rate of absorption of knowledge is improved, as is my total time taken to design things.

Mental Arithmetic is great, agreed.  Are kids even taught it these days?  9V/2k7... it's a lot closer to 3 than it is to 4, so call it 3mA for cash.  For the 120k*22µF one, I learnt a technique when I was in short pants that I remembered as "1 up, 1 down, then 1 down, 1 up".  For the first calc, call it 100*25 = 2500.  Second calc is 150*20 = 3000.  Now split the difference = 2750 which is just over 3% out from the right answer of 2640.  Try another one... 47k*3µ3F.  50*3 = 150.  40*4 = 160.  Split difference is 155 vs real answer, spookily, of 155.1 :D  With a little practice at choosing the number pairs, you can get very close indeed, very quickly, without a calculator.  Just as easy for your example is 12(0)*11*2 and that gets you straight there, because everyone knows their 12-times table, don't they?  Or not...  Because, in my example,  47 is a prime number, factorising is a bit of a non-starter.  Might as well call it 50*3.3 and be done with it - only about a 6% error compared with a probable 10% on the cap?  The thing you have to bear in mind when doing really rough mental scribbling (32% out?) is that if all your errors are in the same direction, by similar factors, you could end up with the circuit doing far more badly than you expected or even not working at all.  When I was a kid in the 60s, we had an exercise book called "10 a Day", the idea being that if you did 10 tricky sums in your head every day, you'd get quite good at it.  "A train leaves Gloucester station at 3:15pm and another one leaves Birmingham at 3:45, blah, blah, blah..."  You know the drill.  Now, where's my iPhone?  It's got an app for that :D
...you fritter and waste the hours in an off-hand way...

Pyr0

Mike, thanks for the brilliant breakdown on the Orange Squeezer, your method of describing the circuit reminded me of a crazy (but great) lecturer I had for electronics back in the late 70's  ;D
and thanks for the maths lesson too.