Analysis of the Tube Screamer

Recent fun-and-games with copies of the Ibanez Tube Screamer guitar overdrive pedal have got me interested in its function to the extent that I've made an analysis of its small-signal frequency response...

Anybody who is discouraged by maths can scroll past ugly equations - there are results of measurements and Spice simulations lower down in this post! You might also find this excellent description of Tube Screamer behaviour more to your taste.

Readers might find the suggestion that linear circuit analysis of the behaviour of an inherently non-linear device is worth performing or reporting ironic. However, one of the defining and differentiating features of the Tube Screamer is precisely the filtering operations it applies to the guitar signal (and non-linear functions thereof). Accordingly, understanding the linear aspects of this "urban legend" is useful - we start with consideration of the "Tone" stage...

This circuit is a (fairly) conventional first-order HF shelving network - adjusting the tone control boosts or lifts the high frequency content of the input signal. However, the presence of the 220nF in the low-pass filter seen in the dashed red box above complicates the circuit - so my analysis is needed. To keep the algebra tidy, I've simplified the picture somewhat (by replacing the paralleled 220nF and 10 kOhm resistor on the input by a single impedance Z_S and by replacing the series 220 nF capacitor and 220 Ohm resistor between the potentiometer wiper and ground by a single impedance Z_P).

It is also necessary to name some nodes and currents, to which the analysis will refer...

The first step in analysing the tone filter is to establish a relationship between the voltage on the tone control potentiometer wiper and the op-amp input(s)...

This relationship will be used in the subsequent solution, so we're giving it a name: "X"...

Notice that X includes some fixed elements (like the impedance Z_P and the total resistance of the tone potentiometer, R_P. However, X importantly includes a variable element, R_p1R_p2 ; X is a function of tone control setting.

Our analysis proceeds by considering the currents at the op-amp inputs...

which leads us to a solution for the frequency response of the Tone stage...

Notice that this solution includes 'X' (which we already know to be a function of tone control setting). The solution in the form above is also itself an explicit function of tone control setting, through the presence of R_p1 and R_p2.

The response of the tone control stage alone is shown in the Bode plot below (produced in MATLAB, by evaluating the solution shown above). The result shows the tone response with the tone potentiometer in extreme positions...

Having solved for the response of the Tone stage, it is simple to go on to develop a solution for the overall frequency response of the Tube Screamer (at least in the small-signal context below the signal amplitudes that start to introduce distortion). Analysis of the "Clip" stage is actually easier than that for the Tone stage...

In the analysis which follows, we assume that the voltage over the diodes is lower than their forward turn-on threshold, in which case they can be ignored. The high-pass filter in the dashed red box of the figure above is loaded only by the very high input impedance of the op-amp's non-inverting input. We can, therefore, obtain its frequency response using the potential divider rule. Thereafter, the op-amp is in standard non-inverting configuration, such that its response is given by a familiar simple rule. The Clip stage small-signal behaviour can be written immediately as...

Various commentators have spoken of the action of the Tube Screamer being largely derived from the fact that the clip stage passes a mixture of the un-processed guitar sound plus the distorted sound - this is seen in the sum in the square bracket of the equation above. I confess that I'm not sure how useful this distinction actually is to understanding the system - particularly as Z_f/Z_in > > 1.

 Now we have small signal responses of the Clip and Tone stages, we can multiply them together to get the overall response of the Tube Screamer (as shown in the equation at the top of this post). But who's to say my analysis is right?

Fortunately, there are ways to check it...

 First, we can follow the lead of others and perform Spice analysis of the system...

Second - and much more interestingly, we can make measurement of an actual Tube Screamer (or, at least, one of my new clones) and compare the result. The graph below shows the magnitude frequency response of the Tube Screamer's small-signal (linear) behaviour, at extreme tone settings. Three traces are shown - one for my analysis, one for Spice modelling and one for actual measurement. You can see they overlay each other, equal (to within expected errors)...

The "Analysis" result in the graph above also includes a few high-pass responses, not described in the text. These are associated with (e.g.) the input and output buffers (implemented by emitter followers in the Tube Screamer) and have very low frequency corner frequencies.

Having spent effort avoiding non-linearity (such that Fourier and Laplace have something to contribute to a small-signal analysis), I took the opportunity presented by having the Tube screamer (clone) connected to some heavy-weight analysis gear to record some of the system's non-linear behaviour...

I generated a 440Hz sine-wave test input. Non-musical readers may remember that 440Hz is an important frequency reference that used to be broadcast on BBC2 with the test card, before wall-to-wall daytime television crowded out the schedule. More musical readers will know that 440Hz is "Concert A"...

With the drive control and tone control on minimum, the output produced in response to the 440Hz input is little different...

Turning the tone control to "Max" allows strong odd-order distortion products through to the output...

With the drive control on "Max", but tone backed off to "Min", there are still strong odd-order overtones produced...

Finally, pushing everything up to eleven boosts the strong odd-order products and also allows some even-order distortion products to be seen...

OK - that's enough building, simulating, analysing and measuring. I really ought to be playing.

...-.- de m0xpd

Send in the clones

Having enjoyed tinkering with my breadboarded rip-off of the Ibanez Tube Screamer, I decided to build some more "permanent" versions...

I knocked up a printed circuit board in Eagle...

A populated PCB is seen along with the original "Dolly" and the first completed clone in the photo below...

The unit is built into a (cheap version of a) Hammond 1590bb diecast enclosure, which I got on ebay from the "Fuzz Shack", who sells the enclosure as a kit with 1/4 inch jack sockets, a d.c. socket and 3pdt push-button switch at a good price (though I'm not using the switch - I've decided to stay with the original 'electronic' switching rather than go for "true bypass", so I'm using a different momentary action push-to-make foot-switch).

 The PCB and the wiring has to be carefully shoe-horned into the enclosure...

R.G.Keen says "The TS series seems to be at its best when driving the input to a tube amplifier" in his excellent discussion of the Tube Screamer circuit - I agree with him...

The two clones aren't both for me (although it is pretty convenient having two Tube Screamers with different set-ups dialled into each unit). Some lucky friend will find one in their Christmas stocking!

 ...-.- de m0xpd

Dolly the Tube Screamer

All this talk of guitars set me thinking about the old days when, as a kid, I used to make replicas of my MXR Distortion Plus ...

Unlike most other areas of audio engineering, guitar amplification is NOT about sound reproduction - rather it is about sound production. The distinction is important; sound reproduction (as in monitoring and what was once called "Hi-Fi") is about generating a faithful acoustic representation of an electronic signal. Guitar amplification, in marked contrast, is part of the system creating the signal. The sound of the guitar amplifier is not (necessarily) at all neutral, introducing components of the overall sound that are important. Most important of these is the family of sounds when (particularly valve) amplifiers are pushed into overdrive, when the resulting distortion can have a pleasant, musical sound in the right context.

Recognition of this fact led to the production of effects pedals (like my old MXR, above) to create (or, at least, emulate) the sound without having to go to the inconvenience (and noise exposure) of over-driving an amplifier. It also led to the appearance of a whole lot of amplifier emulations, exemplified by those built into my new amplifier. Between these extremes of the early, simple distortion (or "fuzz") box and modern complex DSP emulations of classic amplifiers in overdrive there was a whole generation of more complicated distortion effects which I missed over the past few decades. I decided to "catch up" by making a clone of an Ibanez Tube Screamer - thus "Dolly" was born.

The Tube Screamer has three controls; "Drive", "Tone" and a final "Level" control, as seen on my cloned unit...

The schematic can be found at lots of sites over the 'net - start your search here. The most important part of the Tube Screamer (and many other distortion pedals) is the exploitation of the clipping effects of a pair of back-to-back diodes, as seen here in the "clipping" stage of my "clone"...

I used 1N4148 diodes and am (at present) using a TL072 op-amp (I'll change it for one of the original JRC4558s when I get round to making a final version).

Where the Tube Screamer is distinguished from other distortion pedals (including, for example, my old MXR) is in partnering the diode clipping section with filtering circuits - including an adjustable shelving HF section, giving lift or cut to high frequency components both of the original signal and of the harmonics generated by the clipping. The tone section and other aspects of the circuit are seen "round the back"...

Having made the unit, I thought I'd take the opportunity to show some waveforms illustrating its effect on a sinusoidal input (at 2kHz).

Here's the response of the device in "Bypass" mode (the original Tube Screamer has electronic "bypass" switching implemented by some n-channel FETS in a configuration I used before for the Tx audio mute of my Funster Plus rig) controlled by a push button (Dolly uses a 555 in a toggling bistable circuit, whereas the original uses a discrete flip-flop)...

Turning on the unit, with the "Drive" control on max (giving greatest clipping effect from the diodes) and the "Tone" on max (giving HF shelving boost) gives this response (in all the following images I adjusted the "Level" control to keep the output amplitude roughly constant)...

Rolling off the "Tone" to minimum, whilst keeping the "Drive" at maximum makes the waveform "smoother" - and has exactly the same effect on the sound...

Turning the "Drive" to minimum reduces the distortion effect, influencing the sound only when the guitar is played loudly - this sounds more like an amplifier close to its limit, being pushed over the edge into saturation only by the loudest signal components. It sounds nice!

With tone setting on "Max", the effect on the 2kHz sinewave is seen as a tendency toward a triangular wave...

Backing off the tone to minimum, all but removes the visible distortion of the 2kHz waveform...

In truth, all the sounds available from this clone of the Tube Screamer are pretty close to sounds already well-covered by the amplifier emulations built into my new Roland Cube amplifier - but it has been fun to clone Dolly. I might make a PCB and knock up a few copies for friends, just as I did in the old days!

 ...-.- de m0xpd

Cube 40XL Footswitch

I came home from yesterday's G-QRP Mini Convention at Rishworth with (amongst other things) some pushbutton switches from Bowood...

intending to make a footswitch for my new Roland Cube 40XL guitar amplifier. The project was not quite as trivial as expected and other Cube owners may be interested to hear my findings. But first, a little background...

2012 has been for me thus far what Liz might call annus horribilis. Illness has robbed me of some of the energy and enthusiasm for leisure projects and work has been even more of a distraction than usual. Even the virtual organ project (Blogs Passim) has taken a back seat - it is upstairs and it requires that you sit up straight on the uncomfortable, hard bench - hardly the thing when you're not feeling 100%. I did, however, remember that there is one thing that a couch potato can do instead of watching (or even whilst watching) the idiot's lantern - play guitar!

I treated myself to a nice new guitar in celebration of this re-discovered pastime - a Peerless New York.

Then thoughts turned to amplifiers. I already have more than my fair share of guitars and amplifiers, but wanted something that included some of the interesting developments of the past few decades (on-board effects, "modelling" etc). I looked at Fender Super Champs, Line 6 Spiders and the Roland Cube 40XL. I settled on the latter, not least because I could make a simple footswitch to control the many features (rather than pay the manufacturer for one).

So, yesterday I started to knock up a trial footswitch, taking the chance to experiment with an idea for an "enclosure" made of scrap MDF. The piece of scrap that first came to hand was about right for three switches, so that's what I made...

Here's the circuit I used...

(I hope regular readers of this irregular blog will excuse the naive schematics in this post - this material might be of interest to other readers for whom electronics is not the vernacular).

The footswitch worked perfectly in controlling the Effects and Reverb. It also worked perfectly in switching between channels and selecting the alternative "Solo" settings. However, it refused to do anything in controlling the Delay / Looper functions - a particular disappointment as this was the feature I most urgently needed foot control for!

A quick sniff around the net led me to fellow radio amateur Steve, GW1XVC's excellent page on QRZ.com. Steve has also homebrewed a footswitch for the Cube 40XL and his switch works, as he proves in a video on YouTube. His QRZ page included the magic phrase "normally closed", describing the switches he used in his successful footswitch. Mine from Bowood (like all the other momentary action single pole switches in my junk boxes) are "normally open".

I tried "simulating" a normally closed switch (by holding down both switches and momentarily opening one of them) and - hey presto - the looper functions worked under control of my switches. So - I think I need to make an important announcement...

Owners of Roland's Excellent Cube XL amplifiers who, like me, are too cheap to buy expensive commercial footswitches, can use normally open switches for FX/Reverb and Channel/Solo functions BUT MUST USE NORMALLY CLOSED (/"PUSH TO BREAK") SWITCHES FOR THE DELAY/LOOPER functions. 

So - having got that off my chest, what do I do with the apparently useless normally open switches?

I measured the electrical behaviour at the footswitch sockets - open circuit, the control inputs sit at about +3.5V relative to the reference voltage on the sleeves of all the sockets (the footswitch inputs are on 1/4 inch Tip, Ring, Sleeve ('TRS') jack sockets - more commonly known as 'stereo' jacks). When shorted to the sleeve, a current of 450microAmps flows.

I could easily see how to control the looper with the required "normally closed" behaviour if I had some power available, but I didn't want to add a battery to complicate the footswitch - so I came up with a little twist to change the switching behaviour so as to emulate the "normally closed" function using a 2n3904 and a 10k resistor...

For those who don't know, both 2n3904 transistors and 10k resistors are widely available for less money than the switches.

The modified footswitch works perfectly. I just made the change on the two switches used for the Delay/Looper functions - the other switch on my prototype controls the Effects in "normally open" mode.

It works perfectly for me but now for the caveats:

1. It hasn't been tested on another Cube 40XL, so I can't guarantee it will work perfectly for you and...
2. It might not like the EMC-hostile conditions of live stage applications (but I'm sure that any issues could be resolved with a single additional capacitor for each transistor) and... 
3. My footswitch wasn't designed to survive the violent attentions of thrash metal players in Jack Boots. Steve, GW1XVC's rugged construction is more equal to that task!  

Now I'm off to play some guitar

...-.- de m0xpd

Teething Troubles with the Leslie

No sooner than I'd completed the modifications which turned my Leslie 125 into something approaching a 145, I ran into a problem...

Without warning, the amp popped its fuse. On investigation, it turned out to be the mains transformer. I could measure resistances of the order of tens of Ohms where there ought to be isolation - between the secondary, the primary and the core. Also, the secondary centre tap was no longer in the centre - in impedance, at least. Obviously, where once there was insulation there were now some conducting paths.

Maybe I've been lucky, but in 35+ years of tinkering with electronics, I never met a bad transformer before. They just work - or so I thought!

Just my luck - it is easy to find replacement transformers for a 122 or a 147 - they're stock items (especially in the US). But I couldn't find a source for a replacement for my 125 amp's transformer for love or money. Fortunately, Simon at BLS Electronics made me a new one, re-using the pressed steel shrouds from the old unit.

Here are the remains of the original, next to the new transformer...

Usual disclaimer - I don't know Simon or BLS Electronics from Adam - but they did a great job at a great price. The new transformer is now in place and everything was working fine until...

After having played though the newly restored speaker for best part of a day, I noticed that the lower rotor was creeping round in chorale. It would run in tremolo, but ground to a halt at the lower speed. I fiddled about and noticed that if I pushed up the rotor on its spindle (on which it is a friction fit), the rotor would turn again. But, after a few more hours, the old sluggish behaviour returned. Time to strip down the lower rotor...

Here's an exploded image of the rotor from the user's manual...

The drawing indicates that the bearing plate (#511-2 in the drawing above) is fixed in place from beneath the cabinet by two screws. I tilted the speaker enough to get a short screwdriver to the screws, but they didn't have any heads!

Instead, I saw the ends of the screws in some T-nuts. Despite expectations, the bearing unit in my 125 is fixed in from inside, on spacer blocks...

From what I could see, this is how it was made - no evidence of modifications of any kind. I could also quickly see what was slowing down the rotor - especially when it was "low" on the spindle. Here's the top of the bearing assembly, in the middle of which you see the grommet which goes through in the middle of the bearing (numbered 510-3 in the drawing from the user's manual)...

According to the user manual (see exploded drawing above) another grommet (513-2) at the bottom of the rotor bears on this grommet to support the weight of the rotor. Looking at the bottom of the rotor reveals that it had been scraping against the bearing housing, generating the drag that brought the whole assembly to a halt...

Also, I noticed that the bearing housing was distorted in such a way as to bring the bearing lower in the housing - adding to the possibility that the rotor grommet could foul on stationary parts. Look at the deformation in the lower housing component...

The fix was obvious - I needed to keep the rotor higher up the spindle, so the rubber grommet at the base was free. I took a "belt-and-braces" approach and made three interventions.

First, I cleaned and assembled the bearing, avoiding the distortion in the photo above, fractionally moving the ball race and its bearing surface higher.

Second, I inverted the grommet in the bearing, so its unworn lower part is now at the top...

Third, I added a washer between the grommet in the bearing and that on the rotor (between which there is no significant relative movement) to make double-sure there is real clearance between fixed and rotating parts.

The result? The speaker is transformed, with working chorale and much faster acceleration to tremolo. It has been running all day without a hint of trouble. I hope that has fixed it for good.

 I do have some outstanding jobs, most important of which is to cure a rattle/buzz coming from part of the rotor - there's a flared piece (made, I think, of expanded polystyrene) which is moving relative to the other wooden parts and - in so moving - buzzing. I've put some Blu Tack there as a temporary fix.

Excuse me - I must go back to the organ now - this speaker sounds SO good.

 ...-.- de m0xpd

Leslie 125 Modifications

Readers will be aware that I picked up an old Leslie 125 from ebay, just before Christmas. I always had plans for the speaker, but my hand was forced into action when it suddenly started to hum loudly and then popped its fuse - seemed a good cue for a rebuild of the amp and for the modifications I had in mind.

Here's the original speaker, nervously awaiting "surgery"...



My plan was to add a rotating horn, controlled by the MTCLogic speed controller, to take the speaker far from its humble origins to a baby 145. My purpose was two-fold; first to educate me in the ways of Leslies and second to avoid the expense of paying for a "real" 145 (the 125 cost me 31 pounds - you can't buy a 122, a 147 or a 145 for ten times that).

The most obvious external feature would be the additional "slots" in the top of the cabinet - so out came a router...



The result was pleasing enough - my compound cuts with two router bits made a passable impression of real louvres...



Whilst the sun still shone in the outdoor woodwork shop, I turned my attention to fitting some battens to hold the new top shelf. They were made from "available material" - the material having made itself available in a skip next to a building project -  I hate paying for lumber...



 With the battens in place, I could fit my new top shelf...

 

A little more modification gave me a pretty authentic back - with the original labels that proclaim the speaker's lowly origins as a 125...

 

Woodwork completed, I turned my attention to the electronics.

The can capacitor in the power supply filter was replaced, along with some other "mission-critical" capacitors and a power resistor in the power supply filter. There was also a capacitor missing in the amp - bypassing the output transformer's primary at HF and therefore (I suppose) important to HF stability of the circuit.

Also, I added a socket to take 240V and switched 240V to the speed control electronics...



 Here's the amp with its new socket on the side...




With the amp running again, I needed a crossover unit to divide the signal between the original 12 inch unit and the new horn. The stock Leslie crossover looks a bit ramshackle, being built up on a piece of hardboard...

 

I knocked up some brackets to mount the crossover safely on the side wall of the enclosure...



Also seen in the photo above is a (massively over-specified) 240 - 110V transformer, which I'm using to provide the US mains voltage for the MTCLogic speed controller. It is important that I keep this in "stock" condition, as this speaker will be a test-bed for my future work on the new speed control system.

The modified 125 sounds like a dream - it is a joy to use and a pleasure to look at! There are a few more jobs to do (like replacing that massive transformer with something more appropriate and making a motor cover for the top motor to seal the main enclosure), but its is so good to play that these details can wait!

My thanks to George Benton of Benton Electronics for his generosity in sourcing parts, his expertise and his friendship.

 ...-.- de m0xpd