  # Pedal Impedance

## The In and Out of Impedance

Impedance - It's one of the most misunderstood aspects of stompboxes but it is not really that difficult to comprehend. Even beginners understand the concept of resistance and impedance is not much more complex. Impedance is the amount of resistance to an AC signal. The main difference between resistance and impedance is that resistance is the same at any frequency, whether it is 0Hz (or DC) or an AC signal of 10MHz. Impedance can and often does vary with frequency, and is usually a complex interaction of components instead of the value of a simple component like a resistor. A guitar pickup has inductance, resistance and capacitance, and qualifies as a complex signal source. We can combine the effects of those properties into the output impedance of the pickup that is represented here by the Z1 notation. The impedance certainly varies with the frequency of the signal but to simplify our explanations in this article we will use a fixed value for the pickup impedance. The Z1 impedance is in series with the signal source driving the cable.

The pedal input has its own impedance to the AC signal at its input represented here by the Z2 resistance to ground. The circuit, designated by the triangle, provides a drive signal for the output that has its own impedance, Z3. Each pedal has an input and output impedance and the circuit effectively isolates them from each other.

So, how does this have an effect on the sound and signal strength? Let's assume for this example that the impedances are fixed values across the audio band of interest. The Z1 pickup impedance is driving the input of the pedal which has the Z2 input impedance. If we redraw the relation of the circuits we have this: The pickup signal is the 1v at the top and the impedances form a voltage divider! If the pickup impedance (Z1) is 15k and the input impedance of the pedal (Z2) is 100k, then the 1v signal is reduced to about 0.87v, or a 13% loss of signal!

The input impedance of the LPB2 Booster is about 42k so if we have the same pickup as in the last example with a 1v signal and 15k output Z, then the signal at the base of the transistor is reduced to about 0.74v. This is a loss of more than 25% of the original pickup output! As you can see, the input impedance of the LPB2 has loaded down the pickup and caused a severe loss of signal. Let's compare what happens with a different type of booster circuit, such as the jfet amplifier shown here. Since the gate resistance of the jfet is a very large number, the input impedance (Z2) of the circuit is essentially the value of the R1 resistor, or 1M ohms -- we're ignoring the impedance of C1 because it is too small to matter. If we plug this 1M impedance into the formula for the voltage divider illustrated above, we get a 1v input that is reduced to 0.985v at the jfet's gate. This is a much better match than with the bipolar LPB2.

The output impedance of the booster circuit is essentially the value of R2 or 10k ohms. This is not much better than the output of the guitar pickup but it has the advantage that it is consistent across the audio band with very little inductance or capacitance as is inherent in the pickup.

If the input impedance of the jfet booster is raised to 10M, then the signal presented to the jfet gate is 0.999v. Much better! This is the impedance at the gate of the AMZ Mosfet Booster and one of the reasons it is known for giving a crisp, clean full-range sound. Some players who try the circuit say that it adds "sparkle" to the sound when actually all it is doing is allowing the full bandwidth of the guitar pickup to shine through. Now we have the gate resistor at 10M but we need to put a pull-down resistor at the front of the circuit to bleed off DC from the input capacitor to eliminate audible pops when the switch is stomped. As shown here, a 1M resistor has been added at the input... so what is the input impedance? Consider that at audio frequencies the capacitor C1 is essentially a short circuit, which places R1 and R4 in parallel in reference to AC signals. The parallel combination is about 909k ohms! The 10M input has been compromised by the addition of the pull-down resistor. This is a common mistake that is seen on many pedal designs.

At the beginning of the article, we allowed the guitar pickup to have a simple 15k impedance across the band to simplify the examples and calculations. However, the pickup is actually a large inductor which means that the impedance (in Ohms) is smallest at the low frequencies and gets higher as the frequency increases. The impedance of a 100 Hz. signal from the pickup is lower than that from a 1k Hz. note. The rising impedance causes a loss of high frequencies if the input impedance of the circuit is not sufficiently high.

A pickup that has an inductance of 2H will have an impedance of 1257 ohms for a 100 Hz. signal, but that increases to 12566 ohms at 1k Hz. If the pickup is driving the LPB of the previous example, 97% of a 100 Hz. note will be available to the circuit but only 77% of the 1k note -- the highs are being cut. It is even more problematic for higher frequencies and 10k Hz. overtones are reduced to only 25% of their original value! This equates to a serious frequency loss when a guitar pickup is directly interfaced with a low input impedance circuit such as the LPB. In the common situation where you have multiple pedals being used, each has an input and output impedance as shown here. The output Z3 of the first pedal is driving the input Z4 of the second pedal. Output Z5 of pedal 2 is driving the cable back to the amp. Typically Z3 will be a low or moderate value and the full range of sound is easily passed into the second pedal. When both pedals are on, the guitar pickup is isolated from pedal 2 by the circuit of pedal 1. However, if pedal 1 is true bypass and is toggled off, the pickup is directly driving Z4 and pedal 2, so if that circuit does not have a high input impedance, the sound could be adversely effected.

In general, the ideal situation is to have a low output impedance connected to a high input impedance in order to pass the best fidelity signal across the audio frequency band. A unity gain buffer, which has a high input and low output Z, will sometimes be used as a line driver to preserve the full frequency response of the signal.