My aim is to create a quadrophonic panner module for my eurorack system. For this direction, I will create a simple stereo panner mixer (un-buffered input) to give further insight on voltage divider with potentiometer resistors and buffered output circuit system using JFET op amps (TL072/ 078).
Voltage Divider for Two Voltage Outputs
Below is the simulated circuit of voltage divider with a potentiometer. A mono input (about 5v) is divided into two voltage outputs (Left and Right voltage signals). We can add attenuator variable resistor (VR)/ potentiometer to attenuate the mono input before reaching the voltage divider resistor.
Operational Amplifier (Op-Amp): Inverting & Non-Inverting
Below is the Op-amps choose for the stereo panner and TL078 has double dual op-amp (quad op-amp, 4 outputs). There are two types of input-output circuit for the op-amps: 1) inverted op-amp, 2) non-inverted op-amp. The inverted op-amp works by receiving the non-inverted V+ input signals into input #3 (non-inverting input A+) and output the amplified non-inverted signals at input #1 (output A). While the non-inverted op-amp works by receiving the non-inverted V+ input signals into input #2 (inverting input A-) and output the amplified inverted signals at input #1 (output A). The ‘benefit’ of both operating circuit will be described further below.
From above, the left and right divided voltage signal from the mono input will then be summed and buffered with an op amps (non-inverting +). The op amps will detect the incoming voltage, buffered it and re-create a new voltage output according to our desired voltage gain. For non-inverting (+) op amps input, we will have gain formula as follows:
From ideal summing point (non gain) = V in = V out
Gain Ratio = Vin / Vout whereby,
Gain Ratio = 1+ (Rfeedback / Rin)
When the Rfeedback is 0 ohm, the gain ratio is equal to 1 (Unity) = 1 + (0/Rin). You can calculate the values of Rf and R values in google excel to see the Gain Ratio. While, if Rin is 0 ohm, the gain ratio is equal to infinity according to the value of Rfeedback= 1 + (Rfeedback/0). We can have both Rf = 0 ohm and Rin = 0 ohm to achieve Unity gain of 1 and this circuit settings is known as Unity Gain Buffer (Voltage Follower). . This circuit is used for voltage regulator for impedance matching between input and output and useful for summing circuit.
Therefore, non-inverting summing circuit as below.
With inverting op-amp, we can adjust the Rf for gain to be work as volume control from 0 to X gain (reducing to 0 – no sound). Whereby, non-inverting op-amp, adjusting the Rf only works as gain control only from 1 to X gain (1 = original input loudness, adding attenuator at V out – Ground for reducing to 0 – no sound). If using TL078 (quad op-amp) we can apply each left and right audio channel with dual inverting op-amp to produce non-inverting output, whereby the 1st stage op-amp is to invert the non-inverting input and the second stage is to re-invert the inverted signal to non-inverting output and use the second stage inverted op amp as gain/volume control. For simplicity and compact design purpose, I will not include gain or volume control at op-amp output, just attenuators for each input signals.
Audio signal from eurorack is a line level signal at standard of 5V peak to peak (pp). Therefore, I’ve chooses the resistors values of the op amps amplification as follows:
Ri = 100k Ohm
Rvf = 100k Ohm pot
Hence, the gain ratio output will be
A = 1 + (100,000 / 220,000),
A = 2 (times gain factor).
We can add ‘pseudo logarithmic resistor’ in series between the output and Rvf resistor to achieve ‘kind’ of resembles the non-linear potentiometer. Read here.
We can add master volume (attenuator) for both stereo output level using ‘stereo’ potentiometer a.k.a 2-gang potentiometer at the op-amp output line for non-inverting op-amp.
I’ve decided not to set the stereo out as standardized line out level +4dBu (1.228 volts RMS, 3.473 volts pp) Refer to here and here. But to maintain it as eurorack line level +13.2dBu (3.536 volts RMS, 10v pp) by keep the gain factor 2 (that is pretty a lot of gain for now) for 5v DC (3. 536v RMS, 10v pp, AC -5 to +5 v) input. Therefore, I will design output module headphone and standardized +4dBu line out with attenuator resistor for the op-amp output stage to cater the +4dBu down level inspired by Intellijel Outs module (MOD: mute ‘panic’ buttons).
For multiple AC signal summing, we need to keep the offset (0v reference) of the output signal same as to the original input signals (0V in = 0V out whereby, Vo = Vin(1+Rf/(Ri+Rth)) – Vos(Rf/(Ri+Rth)). Read Here, here and here. If we filter out the DC components in the AC signals, we can have AC at its original offset at the output. Read here.
AC VS DC Offset and Components
Next, AC vs DC…. do we need filters for pure AC signal in only? read more here. Panning is used to provide panoramic audio-visual images, in this case, ‘stereo’ image. Since this is an Audio mixer, not a stereo panning CV mixer and therefore, we need to include AC coupling (capacitor) to filter out any DC signals coming into the OP amps and gets amplified (that is anything below 20Hz Fc. = high pass filters threshold) to remove the output offset and reset at 0V reference between peak to peak.
We can add the filtering circuit by placing the capacitor (after the panning VR). If we target the cut off frequency (Fc) below 20Hz in AC signal, and has specific type of resistor (R), we can calculate the value of capacitor (C) needed or vice versa using the formula below:
Fc = 1 / (2π*R*C),
Generally, most modular builders will be using 1uF and 200K ohm resistance for AC coupling in op-amps for 0.7Hz threshold cut-off high pass filter. Adding second filter resistor (R) before potentiometer resistor or any resistor and having signal pass between those two resistor cause a voltage divider output to avoid low voltage output into the inverting input. We need to choose the resistor value carefully usually high value resistor such as 200K or 100K and this will effect the output voltage gain values. If we decrease the filter resistor value, the output voltage gain reduce and vice versa.
If I have 100K ohm and 1uF for the RC, It would give me 1.59Hz cut off. Therefore, we need to match the Fc from both RC and RiCi by using both the same R and C values. Hence, I need to readjust the value of Rf (which is R2 above) to maintain the gain factor of 2. Therefore,
2 = 1+ ( Rf/100K ohm)
2 – 1 = Rf/ 100K ohm
1*100K ohm = Rf.
If 100K ohm and 0.1uF for RC, at 2 gain factor, Ri and Rf will be at 100K ohm. For this case, it is best to change the capacitance value to change the cut-off high pass filter frequency. If we decrease the capacitance, we will increase the cut-off value. For example, 0.1uF or 100nF at 100K ohm will give you 15Hz cut off. However, it is best to keep the cut off frequency as near to 0.00 Hz to remove the DC offset components and retain as much possible AC frequency components (which losing the fundamentals that contributes to the harmonics), therefore 1uF, 4.7uF or 10uF bi-polar (ceramic) capacitor at 100Hz would do the job for that.
We need to check the total sum of maximum input voltage before into +3 non-inverting input op-amp and readjust the resistors after potentiometer to avoid distortion at fixed gain stage. For the module size that I’ll be working, a total of 4 mono inputs is applied.
However, at your own risk: since the output will be AC audio signal, the ‘low 5V DC’ voltage value of reverse audio signal (AC) will not damage blowing up the polarized capacitor that usually has rating above 20v (please read the component data sheet). Would be an ideal to have a non-polarised or bi-polar film or ceramic capacitor for mid to high frequency AC (audio) circuit. I guess, I will get some ceramic capacitor then.
Inspired by Make Noise X-Pan Stereo Mixer; A linear potentiometer panning will provide linear vector image while logarithmic potentiometer panning will provide ‘curved’ vector image. Combining Left and Right panoramic, the linear pot will produce triangle vector while the logarithmic pot will produced semi circular vector. We will explore types of potentiometer values and mechanism to produce desired panoramic audio images for quadrophonic audio imaging in the future, which can be audibly simulated in Pure Data. Back to Vactrol Panner, after spending two days circuit searching, reading and experimenting for vactrol based variable resistance ‘flip-flop’ circuit to produce similar circuit result with 3-pin potentiometer voltage divider, I had managed to find the solution using the Circuit Wizard Simulation Software. Read here. However, we need to fine tuning the resistance ratio between two NPN resistors using voltage probe between the two voltage outputs (Left and Right signals). Theoretically, when the vactrol active [LED bright = LDR resistance low], producing high voltage output for Right signal. We need to duplicate the high voltage output to low the voltage output (2nd output) for the Left signal output. The circuit is based on ‘dark sensor’ LDR circuit using two NPN transistors and mod with two ‘ratio’ resistors only. For consistent variables of the panning, I will replace the 3-pin potentiometer voltage divider with 2-pin with 1-ground mode potentiometer (variable resistor) and divide the voltage using the two NPN transistor-resistor ratio ‘dark sensor’ circuit. The vactrol input will be switchable with the potentiometer using switchtable mono jack (refer to my diy multiplier module).
I did try using the qucs to simulate the LDR (see video tutorial here) but would be more engaging (observable real-time animated results) to simulate LDR and NPN circuit with Circuit Wizard. Alternatively we can do circuit simulation online via https://www.falstad.com/circuit/.
p/s. Interesting reading on panning (signal spread within image field), crossfading (attenuation transition), and morphing (time-based complex signal changes) here.