### Analysis of the Boss MT2 Metal Zone pedal (2)

After a long pause, let’s go on on our MT2 discovery trip. Last time, we analyzed the perfect gyrator that is sometimes used to replace coils.

To analyze the impact of the different replacement for a coil, let’s take the MT2 pre-tone bandpass circuit without the additional capacitor in the feedback loop:

So now the big questions:

• Why didn’t Boss use a coil?
• Why did they use opamps for the tone control section, but transistors for the two tone shaping sections (around the distortion)?
###### A simple bandpass

We can start with replacing the transistor gyrator with a coil $L=1H$ and $R=20\Omega$. I kept the resistor because it’s what the gyrator looks like at low frequencies, but I didn’t try to mimic its high frequency behavior. Obviously a 1H coil is the reason why Boss used a gyrator, such a coil is not adapted for an audio circuit.

To get the Bode diagram, I could just take the equation and ask Numpy to draw it, but as this cannot be done for the transistor gyrator, I’ll use the spectrogram instead, which will give us a Bode diagram for all three circuits.

###### Bandpass with an opamp gyrator

Before we comment the previous bode diagram, let’s create the version with an opamp:

The Bode diagram is now the following one:

We can see a far better behavior for the gyrator in high frequency with no notch effect around 10kHz. Now considering the missing C032, with the full circuit, we should have a nice bandpass behavior, which is what we want to do after the distortion circuit.

So now the crucial question: why a transistor gyrator?

###### Bandpass with an imperfect gyrator

Let’s look at the circuit again:

The Bode diagram is very close to the diagram with the opamp gyrator:

As we have a transistor to drive the gain, we can assume that there is going to be some distortion. Unfortunately, I could not find the actual characteristics of the transistors used in the original Boss MT2, so I decided to use standard transistor values, with a gain of 100 and input a chirp inside the filter:

The top plot is the signal that I input inside the filter and the bottom one is the result. As it is clearly visible, we have some heavy harmonics that are generated from the circuit. There is also clear aliasing showing up, so we know that these circuits will have to be simulated with some oversampling to be used in an actual plugin.

The interesting part is that the second harmonic is present everywhere in the spectrum, whereas it looks like higher order ones are only predominant when the input frequency is low, something like between 500 and 2kHz. This is consistent with the bandpass peak, showing that it’s not just the distortion section that will bing harmonics, but also the pre and post distortion tone shaping sections.

###### Conclusion

First let’s get all the net lists for those who want to redo my analysis:

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 * Vin Vin 0 AC 1 * * Put here your favorite amp model Z3b 2 Vin Vout R044 2 Vout 220k * Gyrator C034 2 3 0.027u R046 3 4 2.2k C035 3 5 0.01u R053 0 5 47k * Put here your favorite amp model Z010 4 5 4
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 * Vin Vin 0 AC 1 * Put here your favorite amp model Z3b 2 Vin Vout R044 2 Vout 220k * Gyrator C034 2 3 0.027u R046 3 4 2.2k L 4 0 1.034
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 * Vin Vin 0 AC 1 Vdd Vdd 0 DC -4.5 Vcc Vcc 0 DC 4.5 * * Put here your favorite amp model Z3b 2 Vin Vout R044 2 Vout 220k * Gyrator C034 2 3 0.027u R046 3 4 2.2k R054 4 Vdd 10k C035 3 5 0.01u R053 0 5 47k Q010 Vcc 5 4 trans .model trans npn(vt=26e-3 is=1e-12 ne=1 br=1 bf=100)

I was very surprised to see the distortion from the transistor gyrator. I was expecting far less generated spectral content, and it’s probable that it’s somewhat different with the real transistors.

What I can say is that the MT2 distortion is not just due to the distortion section. We have lots of asymmetric distortion generated from the two sections surrounding it, each with a different spectral content due to the peak of the filters. As distortion multiplies together, the content of this pedal is far richer than what you get from a SD1 or a TS9 (see the previous posts in this series), and I’m very keen on analyzing the spectral content of the pedal up to the tone control.

Stay tuned for more!

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