Sunday, April 19, 2015

The Nachbaur Diode Limiter, Part 1: Basics

This post is part one in a series of three.
Part two discusses transfer function shapes and resistor selection.
Part three discusses some other variations on the circuit.

As part of a forthcoming project I'm going to call The Phantom Clipper, I revisited the limiter circuit included in the late Fred Nachbaur's "Dogzilla" amplifier.

In Fred's description of the circuit, he says he selected the resistors in the circuit "using a combination of simulated and empirical experiments to arrive at a smooth and easily-managed limiting curve."

In order to make use of it in a much different circuit, I wanted to analyze it a bit more closely, and come up with an algorithm to easily select all the resistors based on the desired transfer function.

Here's just the limiter portion of his circuit (inside the red outline):

It's a clever little circuit that effectively functions as a voltage divider attenuator, and uses a stack of anti-parallel small-signal diodes to switch additional resistors into the attenuator, increasing the attenuation of the divider as the input signal increases:
  • Around 0 volts in, none of the diodes conduct, so no current flows through any of the resistors, and it's as if the divider circuit were not there.
  • As the input voltage increases to reach the forward voltage drop of one diode, D27 switches on to make a voltage divider with R72 on top and R71 on bottom.  Gain = R71 / ( R71 + R72 ).
  • The voltage at the node between R71 and it's adjacent diodes D26 & D27 gets clamped at the diodes' forward drop, so further increases in voltage are attenuated by a divider with R72 on top (still), but R70 & R71 in parallel on the bottom. Gain = R71∥R70 / ( R71∥R70 + R72).
  • This continues until the output voltage reaches the total voltage drop of 5 diodes in series (about 3.5V), where the circuit functions as a divider with all five resistors R67 - R71 in parallel on the bottom.
  • Since the diodes are in anti-parallel pairs, the transfer function is symmetrical for the negative voltages.
Here's a graph of the positive half of the transfer function (green), with the voltage at each diode shown in the other colors.  You can see how the slope of the curve (gain) reduces as each diode switches in. You'll also notice the "knees" in the graph are not hard transitions, but a gradual bend towards the new slope.

So the circuit requires the transfer function to have a few properties:
  1. The transfer function must be monotonic.
  2. For input voltages up to ± one diode voltage drop, about ±0.7 volts, VOUT=VIN (gain = 1).
  3. Parallel resistances mean gain can only decrease for higher input voltage (it can't be an expander).
  4. Knee points (where the gain transitions) must occur at multiples of diode drop for output voltage.
  5. The input voltage where the last stage switches on is not easily determined directly from component values, but only by iterating through each step.
I created a spreadsheet (using Google Sheets) to calculate the approximate transfer function at each of the knee points, based on the resistors. Here it is: Nachbaur Limiter Calculator (resistor input).  You can make a copy to your own Google Drive to edit.

Next post: Selecting the resistors based on the desired transfer function.

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