Tube Simulator - Simulations - Speaker simulator (3/3)

Stephan Möller speaker simulator is based on 4 consecutive sections of low-pass LC filters followed by 2 low-pass RC filters an 2 opamp followers with a potentiometer in the middle for level adjust as the figure below shows.

Since there is no information on frequency response or component values, I decided to do a completely new approach. I chose the frequency response of a good 12-inch guitar speaker and tried to simulate its frequency response with opamp based filters with no inductors which usually are quite large and bulky. The figure below shows the 12-inch Celestion Vintage 30 speaker and its frequency response:

The figure below shows the 12-inch Celestion G12M Greenback speaker and its frequency response:

As it can be seen, SPL (Sound Pressure Level) frequency response ramps up from 70 dB to approximately 100 dB between 20 Hz to 150 Hz, it stays flat at 100 dB until 1 kHz, it has a small 6 dB notch at 1.5 kHz, and it goes abruptly  up close to 110 dB at 2.5 kHz, and then it starts to go down to 80 dB with a steep fall of 10dB at 6Khz. At 20 kHz is somewhere between 60 dB and 70 dB.

In order to replicate a similar speaker frequency response, I designed a 4 section filter based on Sallen-Key opamp topology. I used TI Filter Designer tool to design the speaker simulator filter.

The figure below shows Speaker Simulator schematics.

The resulting frequency response is shown in the figure below:

The design basically consists of four low pass filters with some resonance around 2.5kHz, this enhance frequencies around these resonances and makes the ramp at high frequencies quite abrupt.

Blog update on July 18th, 2014:

The following figure shows approximation in two steps  to final frequency response by using four stages Sallen-Key filters:

There are much more complex speaker or cabinet simulator designs. Some of them can be found at HEXE Guitar Electronics.

To be honest, I am not sure how efficient these cabinet simulators are, because the obtained sound is filtered by the response of the headphones which may vary quite significantly. I guess that the different resonances in the cabinet even if it's open-back and the room itself change the frequency response, so I am not sure how SPL reflects the frequency response of a speaker in a cabinet in a particular room. I guess that first we should get the frequency response in a particular environment, not only amplitude but also phase! then we should get the frequency response and phase! of the headphones (which may vary depending on the model) specially if they are Dr. Dre crap!! and then we should be able to implement a filter that is able to compensate headphones response to reproduce cabinet speaker and room response.

Tube Simulator - Simulations - End stage amplifier (2/3)

End stage amplifier simulations

The figure below shows the schematics of the VoxAC30 end stage amplifier. It starts with a 2-band equalizer for bass and treble and a switch  for equalization shift that adds a deeper notch in the mid tones when activated.

It is followed by an amplification stage based on two 12AX7A valves. It is a valve version of a differential amplifier. It is followed by the high power end stage amplifier based on 4 EL84 valves that feeds the audio transformer and the speaker.

The figure below shows the schematics of the Tube Simulator end stage amplifier. It starts with an almost identical 2-band equalizer, where the values have been scaled to have the same frequency response but more reasonable values. Capacitor values have been multiplied by 100, from 56 pF to 5.6 nF and 22 nF becomes 2.2 uF. Resistor values have been divided by 100 to keep the RC ratio and the same frequency response, so 100 kohm becomes 1 kohm, 10 kohm becomes 100 ohm, and the 1 Mohm potentiometer become 10 kohm. The 2-band equalizer is followed by an RC high pass filter (100 nF, 24 kohm)

The Tube Simulator end stage amplifier consists also of two amplifier sections but opamp based.
Unity gain opamp amplifiers are used to separate each section. Unity gain has been used instead of followers to allow some gain adjusting between sections if required.
The first opamp section includes soft clipping based on silicon diodes plus negative clipping based on germanium plus a series resistor. Another RC high pass filter is added afterwards.

The second opamp section includes soft clipping based on silicon diodes followed by another RC high pass filter.

The following plot compares the time response of a 400Hz sinusoid exponentially decreasing with 50Hz time constant after the 2-band equalizer (top plot), first amplifier section (middle plot) and second amplifier section (bottom plot) of the end stage amplifier for tube simulator (green trace) and AC30 valve amp (red trace).
Different voltage levels have been scaled for comparison.

The following plot shows frequency response from 10 Hz to 20 kHz . Frequency response of Tube Simulator matches that of Vox AC30 amplifier. Different voltage levels have been scaled for comparison.

Tube Simulator - Simulations - Preamp (1/3)

This work is based on Stephan Möller Vox AC30 Amplifier Simulator. It is basically a reverse engineering of his work, so it is fair to start by giving credit to his amazing work. Some schematics can be found on the internet with incomplete component values.

It consists of three stages:

• Preamplifier
• End stage amplifier
• Speaker Simulator

In order to implement a reverse engineering of this project I created an LTSPice simulation of a simplified version of the real VOX AC30 amplifier and an equivalent LTSpice simulation of the tube simulator. I tried to adjust the component values in order to obtain a similar time and frequency response in both circuits for each stage.

Let's start with the Preamplifier stage.

The Preamplifier stage

The Vox AC30 preamplifier consists of two valve amplifier stages, a first stage with one 12AX70 valve followed by a second stage with two 12AX70 valves with a gain potentiometer between both amplifier stages.

These are the schematics for the Vox AC30 preamplifier:

The Tube Simulator preamplifier also consists of two amplifier stages but opamp based and a gain potentiometer between them.
The first opamp stage includes soft clipping based on zener diodes in the opamp feedback with different voltage values to provide some unbalanced clipping or saturation at positive and negative values. I found that a 6.2V and a 4.3V zener where more adequate to match VOX AC30 response. Between the opamp and the gain potentiometer there is a positive hard cliping section based on a Schottky diode with a series resistor. A high value of 470K is used that quite mitigates the diode clipping. This part is quite tricky because actually does not match valve response but having an important clipping affected negatively the next stages.

The second opamp stage includes 4 different types of soft clipping blocks:
Two blocks (positive/negative) based on 2.7V zener diodes + silicon diode in series (not sure the silicon diodes are any useful here) + series resistor (470 ohms / 10 Kohms)
One block based on a germanium diode + series resistor (91 Kohms)
One block based on a 2N2907 PNP transistor with biased base (Rq1 = 47 kohms). Real implementation of the bias will be explained later in the pratical implemention of the circuit.

The figure below shows the schematics of the Tube Simulator preamp:

The following plot compares the time response of a 500Hz sinusoid exponentially decreasing with 50Hz time constant after the first (top plot) and second (bottom plot) stage of the preamplifier for tube simulator (green trace) and AC30 valve amp (red trace). This is a bit tricky, but positive clipping is reduced in the tube simulator for a better stability and signal matching in the next amplifier stage. Voltage levels are higher in the valve amp, so signals are scaled for comparison.

 As it can be observed in the next figure frequency response from 10 Hz to 20 kHz matches very closely.