I was curious to study how does the RAT pedal works because I needed a second distortion pedal and just didn’t want to remove the one installed on my pedal-board each time. So I first had the idea to clone it, meanwhile with the original components (not those that are used nowadays), and with a negative centered DC socket, to make it compatible with my Boss power supply. However, by investigating a bit on internet, I figured out that some people proposed interesting modifications on the RAT, and I decided to try them on my protoboard. The results were satisfactory for some of them to my ears. Thus, I decided to make my version of the RAT including those modifications and I want to share the results here.
Figure 1: The ProCo RAT
The Pro Co RAT is a distortion pedal for electric guitar designed at the end of the 70’s that became very popular at the beginning of the 80’s . It’s circuitry is quite simple, we can divide it in four blocks: distortion stage, tone control, output stage and power supply (see ref. 2 and figure 2). Actually, the RAT is still available, but some of the electronic components have been changed. Indeed, in the new model the operational amplifier OP07DP of Texas Instrument substitutes the original LM308 op-amp. On the other hand 1N4148 diodes substitutes the 1N914 clipping diodes .
Figure 2: RAT pedal schematic (from http://www.electrosmash.com/proco-rat)
In this article, we deal with two modifications on the RAT (you can see a list of possible modifications in Ref. 1 for example). In the first one we have changed the Si (silicon) clipping diodes by Ge diodes (germanium) and red LEDs (Light Emitting Diodes). In the second one we have short-circuited one resistance connected to the operational amplifier, leading to a thicker bass response. The goal here is not to give a detailed explanation of the overall electronic circuit. For those who are interested, Ref. 2 is full of interesting information giving the schematics, the original components of the oldest model and some explanation of how does the circuit works. Here we just want to address the points that are needed to understand the modifications mentioned above. To our knowledge those points are not addressed in detail elsewhere . Finally, at the end of this writing I provide the perfboard drawing I designed to fabricate my own model.
Theory of distortion
Following ref.3: “The word distortion refers to any modification of wave form of a signal, but in music it is used to refer to nonlinear distortion (excluding filters) and particularly to the introduction of new frequencies by memoryless nonlinearities. In music the different forms of linear distortion have specific names describing them. The simplest of these is a distortion process known as “volume adjustment”, which involves distorting the amplitude of a sound wave in a proportional (or ‘linear’) way in order to increase or decrease the volume of the sound without affecting the tone quality. In the context of music, the most common source of (nonlinear) distortion is clipping in amplifier circuits and is most commonly known as overdrive. “Soft clipping” gradually flattens the peaks of a signal and de-emphasizes higher harmonics. “Hard clipping” flattens peaks abruptly, resulting in higher power in the higher harmonics. This is generally described as sounding “harsh”.”
The following graph illustrates this statement showing a 440Hz wave in black, clipped by some circuitry in red.
Figure 3: Sine wave (black) and clipped sine wave (red)
The clipping of a signal can be produced easily with one diode conected forward between the signal and the ground. See figure 4 for an illustration.
Figure 4: clipping of an electric signal with a diode (http://www.electronics-tutorials.ws/diode/diode-clipping-circuits.html)
In this configuration, to make it simple, a diode is a switch that is open, that is to say it doesn’t allow the current to flow when the voltage at its leads is less than 0.7V (for silicon based diodes). If the voltage of the signal exceeds 0.7V, the diode acts like a closed switch and the current will go to ground. As a consequence, when the signal is less than 0.7V, the signal voltage is not modified, but when it exceed 0.7V, it is flattened to 0.7V. With one diode we will have an asymmetrical clipping, whereas with two identical diodes mounted in inverse parallel, we will have a symmetrical clipped output as shown by the red curve in graph 3.
Changing the clipping diodes of the RAT
In the figure 5 we show the schematic of the pedal where both modifications treated in this article have been circled in red. We first deal with the clipping diodes substitution.
Figure 5: schematic used for the fabrication of the modified RAT
As said before, when the signal is larger than the threshold voltage of the diode (typically 0.7V for Si diodes), the signal gets flattened. This leads to an enhancements of the produced harmonics and to a distortion of the sound. If we choose a diode with a different threshold voltage, the amount of distorted signal will vary. For example, if we take a red LED (Light Emitting Diode), whose threshold voltage is around 1.9V, the flattening effect of the signal will occur only when the signal is above 1.9V. This means that we should expect a less distorted signal. Maybe more like an overdrive. An other thing to expect is that the intensity of the signal should be larger than with a Si diode. Indeed, in figure 3, we can see that when the signal is flattened, the signal amplitude is reduced. On the contrary, if we take now a diode with a smaller threshold voltage, like a Ge (Germanium) one, whose threshold voltage is about 0.3V, we should expect more flattening of the signal thus a more distorted and compressed signal, and a lower intensity.
The following video illustrates the effect of changing the clipping diode material on the sound (no additional treatments on the sound have been added like reverb, compression, equalization, etc…):
Filtering modification of the RAT pedal
We want here to understand how does R5, R7, R8, C6, C10 and C11 actuates on the audio spectrum of the circuitry. Instead of finding a literal expression of the gain versus frequency evolution, we try to get an intuitive understanding of what is happening here.
Simple description of the behaviour of a capacitor
What we have to know is that a capacitor is a component that behaves differently in function of the frequency of the signal that arrives to its terminal. Without going to much in details, a capacitor is an insulator (material that doesn’t let the current flow through it) embedded between two metallic films. When one applies a constant voltage to a capacitor, as it won’t let the electrical current passing through it, the electrons of the electric current generated by the battery will accumulate on one side of the insulator. The other side will be depleted of electrons (or we can say it is accumulating holes). So, the capacitor is getting charged electrically. The time it needs to be charged will depends on the value of the capacitance C of the capacitor and of the resistance R that we choose to put with it. Typically this time is given by the product R x C (in seconds). If our signal doesn’t vary with time, or very slowly compared to the RxC product, the capacitor stays charged and thus “blocks” the signal variation. It filters that kind of “slow signal”. However, if the signal varies very fast, so fast that it doesn’t give the time to the capacitor to get charged, this signal will “not see” the capacitor and the information will pass through it. So, the fast variations are not filtered by it.
To resume, we can “say” that a capacitor acts like a switch that is opened for low frequencies and closed for high frequencies.
The definition of what we consider low and high frequencies depends on the value of R and C. As said above, the characteristic time of charging of the capacitor is given by R x C. We can define a cutting frequency f0, such that a capacitor will let pass the frequencies that above f0. It can be found easily that f0=1/2πRC. If RC is large, 1/2πRC is small, thus f0 is small. On the contrary if RC is small, 1/2πRC is large and f0 is large.
An audio signal can be seen as a sum of sine waves that have different frequencies and amplitudes (see Fourrier transformation for more details). The association of a resistance and a capacitor will create a filter, “blocking” the frequencies that are on one side of f0 and “transparent” to the frequencies that are on the other side. By choosing the right values of R and C, we have a control on which frequencies we want to filter.
Filtering part of the RAT
Let’s come back to the circuitry of the RAT pedal, and focus on the filtering part of it. It is represented in figure 6.
Figure 6: the operational amplifier environment
As we have commented before, we can model the behaviour of a capacitor as an open switch for the frequencies of the signal smaller than the 1/2πRC quantity, and a closed switch for the larger frequencies. Let’s apply this model to the circuit of figure 6, composed by three R-C couples: R7-C10, R8-C11 and R5-C6. We have R7=560 ohms, R8=47 ohms, R5 is a 100kohms potentiometer, C10=4.7 µF, C11=2.2 µF and C6=100 pF.
We can calculate their associated cutoff frequency by calculating the quantity 1/(2πRC).
- For R7-C10, we find f1=1/(2p × 560 × 4.7e-6)=60 Hz
- For R8-C11, we find f2=1/(2p × 47 × 2.2e-6)=1539Hz
- For R5-C6, we find f3/(10e3 × 100e-12)=159kHz where we have arbitrary choose 10 kHz for R5.
We note that f1<f2<f3.
Then, we will consider 4 cases, depending on f with respect to f1, f2 and f3. Before going further, we want to come back briefly to the basics of OA (operational amplifiers). Having this in mind, the following will be more straight.
Figure 7: typical inverting amplifier problem
In the figure 7 we have represented the case of an inverting amplifier. This configuration is called inverting because the resistance R2 connects the output of the OA to the negative input. We can apply the Millman formula to find that:
Thus we find that the relation between the output voltage Vo and the input voltage Vi is:
Let’s now come back to our problem:
- If f<f1, we are in the case where all the capacitors are equivalent to an open switch (see figure 8).
Figure 8: case f<<f1
We can use (1) by substituting R2 by R5 and R1 by a resistance with an infinite value. In the equation (1), if R1 is very large compared to R2, R2/R1 is very small, tending to 0. Thus, we find that Vs=Vo. So at very low frequencies, the gain G, which is given by V0/V1 is G=1.
2. If f1<f<f2, we are in the case where the capacitors C11 and C6 are equivalent to an open switch and C10 is like a closed switch (that is to say a conductive wire, see figure 9).
Figure 9: case f1<f<f2
In this case we substitute R1 and R2 in (1) respectively by R7 and R5.
Thus we find that Vo=(1+R5/R7)xVi. So the gain G=1+R5/R7=1+10k/560=19
3. If f2<f<f3, we are in the case where the capacitor C6 is equivalent to an open switch and C10 and C11 are like a closed switch (see figure 10).
Figure 10: case f2<f<f3
In this case we substitute R1 and R2 of (1) respectively by R7//R8 (// is an abbreviation standing for R7 and R8 in parallel) and R5, with R7//R8=R7xR8/(R7+R8)=560×47/(560+47)=43 ohms.
Thus we find that Vo=(1+R5 / (R7//R8))xVi. So the gain G=1+R5 / (R7//R8)=234.
4. If f3<<f, we are in the case where all capacitors are equivalent to a closed switch or a conductive lead (see figure 11).
Figure 11: case f3<<f
In this case we substitute R1 and R2 of (1) respectively by R7//R8 and a 0 ohm resistance. So it is easy to demonstrate that we come back to the case Vo=Vi and thus G=1.
Simulation of the filtering circuitry
We have performed the simulation with PSPICE on this portion of the schematic:
Figure 12: schematic used for the PSPICE simulation.
The signal is modeled by the sine wave generator of amplitude 1V. We sweep its frequency from 0.01 Hz to 108Hz (yes, well above the ear response), and we measure how does the output voltage varies with frequency.
The following graph shows the results of the simulation, showing the variation of the gain with the frequency of the signal:
Figure 13: results of the PSPICE simulation on the gain evolution vs frequency
The black symbols represent the results of the PSPICE simulation. To compare with the simple model we have developed above, we have also drawn the 3 values of gain (G=1, 19 or 234) and the 3 cutoff frequency (f1=60, f2=1539 and f3=159kHz).
We can check that the simulation agrees well with our academic model: well under 60Hz and well above 159kHz we find a unity gain. Between 60Hz and 1539Hz we have a first step of gain in agreement with our result around 19, and we reach a maximum around 234 between 1539Hz and 159kHz.
We now represent the simulation for different values of resistance of the distortion potentiometer, within the ear response (20Hz-20000Hz):
Figure 14: Results on the PSPICE simulation on gain evolution vs frequency for different values of the distortion potentiometer
We see an increase of the overall gain with the resistance of the distortion potentiometer, with always a larger gain for high frequencies.
Knowing this, what is interesting us now is to change the gain spectra. With our understanding on the influence of the resistances and capacitors on the gain shape, we have performed a PSPICE simulation by short-circuiting the resistance R7 (560 ohms) or the resistance R8 (47 ohms). The following figures shows the results we have found:
Figure 15: Results on the PSPICE simulation on gain vs frequency with R7 or R8 short-circuited compared to the default case.
The simulations shows that short-circuiting R7 (560 ohms) has not a big influence on the gain spectra. However, by short-circuiting R8 (47 ohms) there is a clear change: the spectra is flatter. The high frequencies are not so much amplified, which should lead in theory to a much bass-rich sound, or muddy sound, with a lower overall intensity. We have made the following video to check this:
Construction of the pedal
Finally we show the pedal from the inside. We have used original components.
Figure 16: the modified RAT from the exterior and interior.
An easy way to fabricate your pedal without using chemicals product is to use a perfboard. The following figure shows the one I have designed (I tried to put the components as close as possible to economize space). On the left hand side is given the top side of the perfboard. On the right hand side we can see the bottom side. This view is useful, because once the components are soldered, they have to be connected through tin rails. The bottom view gives a direct view of how those rails have to be made.
Figure 17: top side and bottom side of the perfboard. “Input” connects to the 3PDT switch, “9V batt” to the 9V battery or to the ground of the DC socket (that we want negative centered). “Led” connects to LED anode (+), “ground” connects to chassis. “9V” points have to be connected together with a wire. “Tone”, Dist”, “Vol” connect to each of the three potentiometers. S1 connects to the three ways rotary switch. S2 connects to a regular switch.
The main foot switch to switch the effect on is a 3PDT to allow true bypass, the wiring is explained in an other post (see here).
Introduction to wha-wha and gyrator:
There are a lot of information that one can find on internet about wha-wha pedal: how does it work , schematics [2, 3]. “What a wah does is clear – it is either a bandpass filter or an overcoupled lowpass filter that exhibits a resonant peak just at its lowpass rolloff frequency. The resonant peak can be moved up and down in frequency by the player, and this makes for a striking emulation of the human voice making a “waaaah” tone, or its tonal inverse, “aaaooow” , as ilustrated by the frequency response in figure 1.
Figure 1: theoretical frequency response of a wha-wha pedal (from ).
The general way to create the resonance peak is using an RLC filter (R: resistance, L: inductance, C: capacitance), see for example figure 2.
Figure 2: example of a wha-wha pedal circuit (from ).
Although resistance and capacitance are easy to find, the required inductance has to occupy a non negligible volume, and/or are expensive. However, it is possible to simulate an inductance with an operational amplifier. The circuit is named a gyrator, which is composed by an operational amplifier, and a set of adequate resistances and capacitors, as can be seen in the figure 3. When associating those components, we can calculate that the resulting behaviour is equivalent to the one of an inductance of value L1=R1xR2xC1, in series with the same resistance R1.
Figure 3: principle of the gyrator circuit.
The idea of replacing the inductance in figure 2 by a gyrator has already been suggested in the excellent book of D. Dailey , see for example figure 4, where a circuit without transistors but only an operational amplifier is used.
Figure 4: the inductance of figure 2 is replaced by a gyrator circuit (inductance simulator) (from ).
To our knowledge, there are no commercial wha-wha pedal based on that kind of circuit. The present article deals with the practical realization of the circuit proposed by D. Dailey, where we have implemented some modifications. Finally, some sound samples of the fabricated wha-wha pedal are presented.
The few modifications brought to figure 4 are that first, we want to supply the operational amplifiers with a single supply (one 9V battery instead of two), as it is obviously a gain in space and perhaps money -it is not sure that the consumption will not be higher with only one battery. This has to be clarified in the future-. Also, we have added some coupling capacitor to reduce the overall noise. The resulting circuit of the gyrator-based wha-wha with single supply is given in the figure 5:
Figure 5: Schematic of the gyrator-based wha-wha that will be fabricated.
Varying the value of the potentiometer R4, the resonance peak moves in frequency. To visualize it, we have performed some SPICE simulations. Those simulations appear in the figure 6. Increasing the resistance R4 from 9 ohms to 90 kohms, we see a clear evolution of the resonance peak from high frequency to low frequency, which is what we require to obtain the wha-wha effect. We also see a displacement of the bandwidth and its narrowing by increasing R4.
Figure 6: simulation of the evolution of the filter by varying the wha potentiometer (R4).
We have also looked at the influence of some components on the spectra, as can be the non-desired gain loss of the output coupling capacitor C9 (see figure 7). If we look to the black curve, we see a non-zero signal at very low frequencies which corresponds to audible noise. Introducing a capacitance in series leads to low pass filtering, which is good to remove the low frequency noise, but that lower our signal if the capacitance value is too low. Following the results shown in figure 7, we have chosen a capacitance value of 1uF which seems a good compromise to filter the DC noise while keeping the signal level shape.
Figure 7: simulation of the filter spectra for various values of C11.
The circuit has been soldered on a perfboard for ease of use (see figure 8). The ensemble -perfboard/9V battery/potentiometers- has been inserted inside an old and cheap volume pedal. As the enclosure was not so big, we had to find a way to solder the components as closed as possible.
Figure 8: (Up) the parts were assembled on the perfboard that way, in order to gain space. The + and – symbols refer to the 9V battery pins, GND stands for ground, 9V’s dots and 4.5V’s dots have to be linked together by a wire. IN stands for the input, audio dot connects to the R2 potentiometer and wha’s dots connect to the wha potentiometer R4. (Down) the wiring of the 3PDT switch.
The result can be seen in figure 9. The on/off switch is a 3PDT switch to avoid tone sucking (read Ref. 5 for more information on true bypassing). The only problem we get that we have to mention is a pop when effect is switched ON. Further investigation are under way to solve this problem. Also we want to mention we first used a TL07x series operational amplifier at the beginning, and experimented an unexpected oscillation behaviour, which physical origin could not be determined. It occurred when having the wha potentiometer on the more resistive position and switching the pedal ON. This oscillation behaviour disappeared completely just by changing the operational amplifier with an other type, the NE5532P. Thus, this behaviour is attributed to the TL07x.
Figure 9: final result. The potentiometer on the right is the potentiometer R2 controlling output volume. On the left, there is an additional potentiometer that doesn’t appear in figure 5. The idea was to vary the value of R3 to be able to vary manually the value of the equivalent inductance. But the result was quite disappointing, so it has been removed from the figures of this article.
As a sound test, we present finally this video:
It could be interesting to compare this gyrator-based wha-wha with a commercial wha-wha (based on conventional RLC filter). This may be the object of a new article.
Conclusion and perspectives:
Here is a famous intro of one Jimi Hendrix song, freely developed:
And more sound samples:
You will find more music on www.olivierjambois/music
 Denton J. Dailey, Electronics for guitarists, Springer
This work has to do with the amazing observation that under very small dimensions, rules governing physics at our scale change, due quantum effects. I was studying the case of silicon during my PhD studies. Silicon, the material constituting more than 90% of microelectronic components, is an indirect bandgap material. One consequence is that it is not able to emit light. However, finding a way to make silicon able to emit light would be a great deal, as information could be transmitted by the light generated by silicon-based component, and not by electrons, as it is nowadays the case in computers for example. The main advantage of this would be a faster communication, as light goes much faster than electrons. In the middle of the 90’s, an investigation group leaded by Leigh Canham got light from porous silicon, and proposed the theory that when silicon dimensions are reduced to a dot that has less than 5 nm diameter (nm stands for nanometers, 1 nanometer=1/1000000 millimeter), selections rules relax and bandgap opens, making silicon able to emit efficient light in the visible range (visible to human eye). My thesis deals with the study of how it works by studying the luminescence of Si nanocrystals. My PhD work was defended publicly in 2005.