On Negative Impedance

Impedance is a concept in electrical engineering that all EE graduates learns. It is an extension to the resistance from DC field to AC field. 

It is common for engineering to describe a voltage source, which maintain the voltage regardless of load condition as 0 ohm output impedance. Also, people describe a current source as infinity impedance, which maintain the output current regardless of load conditions. 

In reality, the physical realization of a voltage source is in on the source/emitter output of a transistor, when it works in linear regime. While, the drain and collector plays as the current source in physical world. 

Negative is a weird word that often confuse people, from a little kid trying to understand what is smaller than 0, to weird situation like what is even a negative absolute temperature. 

In electronics domain, negative impedance is rarely talked about. Part of the reason is that untamed negative impedance leads to oscillation, which people often hated, unless they are in the business of making a clock. The founder of SpecialtyCircuit LLC decided that he should write something about negative impedance, so that he can promote his failing endeavor to commercialize his beautiful headphone amplifier. So, here we go. 

The real world application of negative impedance.

1. voice coil driver that regulate the coil motion velocity to input audio signal [add link to headphone advertisement page]
2. economical motor speed control in cassette tape motor drive to maintain tape moving speed [add datasheet to obsolete IC]
3. active damping in vibration control [add citation to LIGO]
4. resonant damping in motor control [add link to galvo driver]
5. faster current settling in deflection coil control [add link to spice simulation of inductor driver]

What does negative impedance even mean?

In Ohm law, we all know U = I R. When R is a positive normal value, the more voltage you applied across a resistor, the more you will get out of it. While, for negative impedance, the more voltage you apply across a device, the less current will flow through it, that is what it means. 

In the traditional sense, people often assume that the impedance/resistance sort of stays as a constant value. Well, in reality, resistance/impedance can change over frequency, DC biasing value, etc. It need to be treated very clearly that, negative impedance does not necessary happen over all operating condition, it often only behave within a certain frequency range, or operating area. The typical use case of negative is within a narrow operating area, not in all operating conditions, often within the application use case regime. 

In the voice coil/headphone driving use case, a synthetic negative impedance is introduce in the driver, such that the intrinsic resistance, plus inductance sometime, is cancelled out, leaving only the motional impedance seeing the control signal. The operating frequency range is set to slightly broader than the human hearing range. 

When talked about negative impedance, it is unavoidable to discuss about positive current feedback, because that is really what's happening when a synthetic negative impedance functions. Hopefully, the reader still remembers that we mentioned a negative impedance is when the driving voltage increases with current decreases. In a normal negative feedback system, when the command change direction, the actuator will follow it. In the case of positive feedback, the actuator will act against it. If the actuator acting against the command change very hard, it will results in an oscillator. The magic in negative impedance drive is that the actuator need to act against the command change just enough, to avoid the oscillation regime.