Building a Eurorack State Variable Filter – Part 1
Filters are the heart of subtractive synthesis and an essential module in any Eurorack setup. While oscillators provide raw, harmonically rich waveforms, it is often the filter that shapes them into something dynamic, expressive, and musical. In many classic and modern synth designs, it’s the filter — not the oscillator — that gives an instrument its instantly recognisable character.
A State Variable Filter (SVF) is particularly versatile, providing low-pass, high-pass, and band-pass responses from a single circuit. This makes the SVF a powerful and flexible tool for sound design, whether you’re gently sculpting timbre, carving space in a mix, or adding movement and animation to a patch.
With that versatility in mind, we set out to design a DIY Eurorack state variable filter built around the venerable LM13700 Operational Transconductance Amplifier. Rather than chasing super aggressive self-oscillation or screaming resonance, our goal was a filter that feels smooth, predictable, and musically controlled. This design won’t shout or demand attention; instead, it politely suggests that your signal might like to roll off a little top end with just enough self-oscillation to add character.
In this guide, we’ll build LM13700 based State Variable Filter using the N8 Synth 8HP Eurorack Prototype Kit. The module is based on two OTA low-pass stages, with resonance carefully shaped and limited using zener diodes to keep the response stable, musical, and well behaved — perfect for everyday patching.
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Eurorack State Variable Filter Schematic & Module Layout
What's a State Variable Filter Anyway
The term state variable filter comes from the idea that a filter has a “memory” of what it has been doing. The voltages stored by the filter’s capacitors are constantly changing, and together they describe the filter’s current state. In more formal analysis, these voltages are treated as variables, which is where the term state variables — and the name of the filter — comes from. Here, we will not delve deeply into math but aim to provide a conceptual understanding of how the filter works as a starting point for your experimentation.
The core of a state variable filter (SVF) is a summing amplifier followed by two op-amp integrator stages. As the name suggests, an op-amp integrator is an operational amplifier circuit that performs the mathematical operation of integration. In practical terms, this means the output voltage depends on how the input voltage changes over time, rather than simply following it instant by instant.
If that sounds abstract, it helps to think about what the circuit is physically doing. The input signal is applied through a resistor to a capacitor in the op-amp’s feedback path. When the input voltage is positive, current flows into the capacitor, charging it; when the input voltage is negative, the capacitor discharges. The op-amp’s output follows the capacitor’s voltage (inverted), producing a smoothed version of the input signal.
Now consider how this behaves with different frequencies. For a low-frequency sine wave, the signal spends more time above and below zero, giving the capacitor more time to charge and discharge. This results in a larger output signal. For a high-frequency sine wave, the signal changes direction more quickly, so the capacitor has less time to charge, resulting in a reduced output amplitude.
Because of this frequency-dependent behaviour, an op-amp integrator acts as a one-pole low-pass filter, with the cutoff frequency determined by the resistor and capacitor values. In a state-variable filter, two such integrators are cascaded to form the filter’s core.
When an audio signal passes through two identical one-pole low-pass stages in series (both set to the same cutoff frequency), the result is a two-pole, 12 dB/octave low-pass filter. This gives us the familiar low-pass response, but on its own it wouldn’t be very exciting.
What makes the SVF so useful is the way feedback is applied around these integrator stages. By feeding signals back from different points in the circuit and mixing them with the input, the filter can produce multiple responses simultaneously. Subtracting the low-pass output from the input produces a high-pass signal. This high-pass signal then feeds the first integrator, whose output naturally has a band-pass response. Meanwhile, the output of the second integrator provides the low-pass output.
Because all three outputs — high-pass, band-pass, and low-pass — come from the same filter core, they stay perfectly related in frequency and phase, which is one of the defining and useful features of a state variable filter
In a state variable filter, resonance is set by the amount of the filtered signal fed back into the summing amplifier. In our design, we use the band-pass output as a damping feedback path: feeding more band-pass signal back into the summing amplifier “calms down” the response around the cutoff frequency, reducing the resonance peak. Feeding back less band-pass reduces that damping, so the filter rings more strongly at the cutoff — giving higher resonance, and eventually self-oscillation if the damping is low enough. However, this is a “polite” filter design, so we don’t allow it to reach self-oscillation.
State Variable Filter Schematic Overview
Building on the ideas above, let’s look at how this applies to the schematic. A textbook SVF uses two op-amp integrator stages with a fixed cutoff frequency determined by their resistor and capacitor values. To make the cutoff adjustable, we need a way to vary the effective value of one of these components.
Using a variable resistor would allow manual control, but it doesn’t help if we want voltage control as well. Instead of thinking about the resistor only as a physical component, it’s useful to think about what it actually does. In an integrator, the resistor converts an input voltage into a current, which then charges or discharges the capacitor.
An operational transconductance amplifier (OTA) performs the same voltage-to-current conversion, but with electronic control. In the LM13700, a control current (labelled Iabc) sets the amplifier’s transconductance, and therefore the output current for a given input voltage. By using the LM13700 in place of the resistor in the integrator, we create a voltage-controlled integrator whose cutoff frequency can be smoothly adjusted by a control voltage.
Lowpass Filter Stages
Looking at the schematic, we can see two identical low-pass filter stages. Each stage uses one OTA from an LM13700, together with an op-amp and a capacitor to form a voltage-controlled integrator. Because the OTA’s transconductance is set by a control current, this arrangement allows the cutoff frequency of both stages to be controlled with a control voltage.
Focusing on the first low-pass stage, the signal first enters U4C, one of the LM13700’s two OTAs. The OTA converts the input voltage into an output current, with the magnitude of the current set by the control current (Iabc) applied at pin 1. This output current is then passed to the following op-amp integrator, where it is integrated onto capacitor C5, producing a low-pass response.
The LM13700 has high-impedance voltage inputs, so very little current flows into them. However, the OTA operates linearly only over a limited input-voltage range, and distortion increases as the difference between the inputs increases. To keep the OTA operating in its linear region, the audio signal is attenuated using a resistor divider formed by R15 and R18 before it reaches U4C’s inverting input. This limits the input voltage swing and helps ensure the OTA’s output current remains well-behaved. The op-amp U1C then converts this current back into a voltage, ready to be passed on to the next filter stage.
Diodes D1 and D2 are included to limit the maximum amplitude of the band-pass signal being fed back into the filter core. As resonance is increased and the filter begins to ring more strongly, the voltage at the band-pass output rises. Once this voltage exceeds the breakdown voltage of the zener diodes, they begin to conduct and clamp the signal.
This clamping action reduces the effective feedback at high signal levels, preventing the resonance from increasing indefinitely. In practice, this prevents the filter from entering self-oscillation while still allowing a strong, musically useful resonance peak near the cutoff frequency.
The voltage rating of the zener diodes determines how early the resonance limiting comes into effect. A lower zener voltage means the diodes begin to conduct at smaller signal levels, so the resonance is gently restrained sooner. This produces a smoother, more controlled resonance. A higher zener voltage allows the band-pass signal to grow larger before limiting occurs, giving a more aggressive, sharper resonance peak. We’ve used 1N4734’s with a zener voltage of 5.6V, but it is worth experimenting with different values to find a character you like.
Calulating the cutoff of one low-pass filter stages
We said no maths, but this is the useful bit to bung into Excel if you are designing you own filter.
Each low-pass “integrator” stage has an approximate pole (corner) frequency set by the OTA transconductance and the integrator capacitor:
Where:
- is the pole frequency of one integrator stage (Hz)
- is the LM13700 control current (A)
- is the integrator capacitor (F)
- and form the input divider, so the OTA only “sees” a fraction of the input voltage:
Note: this is a practical approximation (the LM13700’s varies with device tolerances, temperature, and how hard you drive the inputs). The cutoff will also shift slightly with resonance, because the outputs are coupled by feedback. The LM13700 datasheet explains the constant 19.2 is related to temperature so the formula assumes we are operating at a steady 25 degrees celsius.
Feedback Loops
The low-pass feedback path is simple. A copy of the low-pass signal is returned to the summing amplifier through a 10 kΩ resistor, R7. Because the summing amplifier’s feedback resistor, R12, is also 10 kΩ, this feedback path has unity gain with inversion.
The inversion ( relative to the input ) is important because it means the low-pass signal is subtracted from the input signal at the summing amplifier. This subtraction removes the low-frequency content, leaving behind the high-frequency components. The output of the summing amplifier, therefore, has a high-pass response. At low frequencies, the low-pass output closely follows the input and cancels it out at the summing node, while at high frequencies, the low-pass output is much smaller, so the input passes through largely unchanged.
The band-pass feedback path is more involved because it provides CV control over resonance. Here, an additional OTA is used as a voltage-controlled gain element, adjusting the amount of the band-pass signal fed back into the summing amplifier. Op-amp U3A is configured as a transimpedance (current-to-voltage) converter, turning U5C’s current output into a voltage signal that can be mixed back into the filter core.
Although the low-pass feedback loop is nominally unity gain, real-world component tolerances and operating conditions mean that the effective loop gain can approach — or even exceed — unity in practice. When this happens, the filter core becomes under-damped and can begin to self-oscillate.
The band-pass feedback loop is therefore used as a damping mechanism. By feeding a portion of the band-pass signal back into the summing amplifier, the filter’s gain around the cutoff frequency is reduced, stabilising the filter core. In synthesiser terms, this is what controls the resonance. Increasing the band-pass signal feedback increases damping and results in a smoother, less resonant response, while reducing band-pass feedback relaxes damping and allows the resonance to increase.
Input Buffer & Summing Amplifier
The input buffer is included primarily to address phase inversion. The filter core inverts the audio signal, which may not always be desirable in the context of a modular patch, especially when signals are being mixed or combined elsewhere. U1B is configured as a unity-gain inverting amplifier, inverting the input phase so that the output signal is restored to its original phase.
At a nominal input level of 10 Vpp, the filter can produce output swings of up to 20 Vpp at high resonance settings. To allow some control over signal levels, an input trimmer (RV1) is included, allowing the signal to be attenuated slightly if required. This helps keep levels sensible and prevents unwanted clipping further down the signal path.
U1A is configured as a straightforward inverting summing amplifier and fulfils the central role of the SVF’s summing node, where the input signal and the various feedback paths are combined to generate the high-pass response and drive the filter core.
Cuffoff Control
The cutoff control section generates the control current (Iabc) used by the LM13700 OTAs to set the filter’s cutoff frequency. The cutoff knob, RV2, and incoming CVs are summed and scaled, then passed through an exponential converter before being converted into a control current. This ensures that the cutoff frequency responds in a musically useful way, where equal changes in control voltage produce equal-sounding changes in pitch or frequency.
The exponential converter is designed to give an approximate 1 V per octave response. Unlike a precision V/octave converter, it does not use a temperature-compensating resistor or matched transistor pair, so absolute accuracy is not the goal here. Instead, the emphasis is on musical behaviour. Trimmer RV5 allows the response to be adjusted to taste.
An exponential converter is used because filter cutoff, like oscillator pitch, is perceived logarithmically by our ears. Without this exponential relationship, most of the cutoff range would be compressed into a small portion of the control travel, making the filter harder to tune and control. The exponential converter spreads the cutoff range more evenly across the knob and CV inputs, giving a smooth sweep.
The resulting control current is applied to the Iabc pins of the two integrator OTAs so that both filter poles track together. The LM13700 allows a maximum Iabc of around 2mA, but we keep well below that limit, at approximately 720 µA. Operating the OTAs at lower control currents improves linearity, reduces distortion, and yields a more stable, musically consistent filter response.
Our MS-20 filter build guide covers this type of exponential converter in more detail.
Resonance Control
U3B is configured as an inverting amplifier and summer, allowing multiple resonance CV sources to be combined. The output of U3B sets the control current (Iabc) for U5C, which in turn determines how much of the band-pass signal is fed back into the summing amplifier.
Because U3B is an inverting amplifier, an increasingly positive input voltage produces an increasingly negative output voltage. The Iabc pins of the LM13700 are approximately 2 diode drops above the negative supply rail (around –10.6 V in this circuit). As the output of U3B becomes more negative, the voltage drop across R20 decreases, reducing the control current flowing into U5C pin 1.
Reducing this control current lowers the OTA’s transconductance, which reduces the amount of band-pass signal fed back into the filter core. In this design, the band-pass feedback acts as a damping mechanism, so less band-pass feedback results in greater resonance.