Definition of Impedance

The definitions are from the book Dynamical Analogies - Olson (Acoustical Research Director of RCA, inventor or pioneer of the ribbon microphone,...)


Electrical impedance is the complex quotient of the alternating electromotive force applied to the system by the resulting current.


(Complex numbers are vectors or 2 dimensional numbers. For example a,b or a+ib, a+jb, x,y or x+iy etc. The X axis is the real axis and Y axis is the imaginary axis. Why using complex numbers? Because it is only when a pure resistance is used that voltage and current are in phase. Reactance on the other hand is 90 degrees out of phase. Try for example moving back and forth a door at various frequencies. You will feel the phase difference between force applied and velocity. A door has mass which is the mechanical systems equivalent of inductance in electrical circuits (systems). You will also feel that the reactance depends on frequency. The higher the frequency the more the door reacts. Ie reactance or the imaginary part of impedance changes.)


Electrical resistance is the real part of the electrical impedance. This is the part responsible for the dissipation of energy.


Electrical reactance is the imaginary part of electrical impedance.


(Inductance and capacitance have reactance, they store electrical energy and may give it back).


Inductance in an electrical system is that coefficient which, when multiplied by 2π times the frequency, gives the positive imaginary part of electrical impedance.


Capacitance in an electrical system is that coefficient which when multiplied by 2π times the frequency, is the reciprocal of the negative imaginary part of the electrical impedance.


Mechanical impedance is the complex quotient of the alternating force applied to the system by the resulting linear velocity in the direction of the force at its point of application.


Mechanical resistance is the real part of the mechanical impedance. This is the part responsible for the dissipation of energy.


(Mechanical resistance is friction)



Mechanical reactance is the imaginary part of mechanical impedance.


Mass in a mechanical system is that coefficient which when multiplied by 2π times the frequency gives the imaginary part of the mechanical impedance. The unit is grams.


(For example trying to oscillate a door at high frequency we may immediately feel what is mass is and what mechanical impedance is).

Compliance in a mechanical system is that coefficient which when multiplied by 2π times the frequency is the reciprocal of the negative imaginary part of the mechanical impedance.


Acoustical impedance is the complex quotient of the pressure applied to the system by the resulting volume current.


Acoustical resistance is the real part of acoustical impedance. This is the part responsible for the dissipation of energy.


Acoustical reactance is the imaginary part of acoustical impedance.


Inertance in an acoustical system is that coefficient which when multiplied by 2π times the frequency, gives the positive imaginary part of the acoustical impedance.


Acoustical capacitance in an acoustical system is that coefficient which when multiplied by 2π times the frequency, is the reciprocal negative imaginary part of the acoustical impedance.


Some notes or examples:


π is the Pythagoras number 3.14...... The quotient of circumpherence to diameter for any circle.


A coil has inductance. I'd tries to keep the current thought it constant. If for example we connect a coil in series with an amplifier output all we wil hear from a loudspeaker will be bass.


The analog to inductance in mechanical systems is mass. A train or a boat or anything that has mass really tries to keep its velocity constant.


Capacitance tries to keep the voltage across it constant. For example we may charge a capacitor. And then light up an Ed gif relatively long time.


The analog of capacitance in mechanical systems is compliance. It tries to keep the force constant. For example our hair protecting our head. Other example is springs which have compliance.


A mass and and spring can oscillate. Friction or resistance damps the oscillation.


So,do a mass inductance connected to capacitance. The tune circuit self oscillates. Resistance damps it until oscillations stop. The heat of a radio transmitter is a capacitance and inductance.


In a analogous way the inertance of a bottle neck and the acoustical capacitance of a bottle volume create a reasonant acoustical circuit. We can hear the reasons at frequency. And we can blow to it and it will produce a tone.


Putting some cotton in the neck will damp the oscillation as this is acoustical resistance. It converts the vibrations of electrets to heat.


See also impedance matching in the next euroelectron post


References:


Dynamic Analogies - H. F. Olson


Introduction to System Dynamics - Shearer, Murphy, Richardson - MIT


Engineering Circuit Analysis - Hayt, Kemmerly - McGraw-Hill


The Feynman Lectures on Physics - Feynman, Leighton, Sands


Conceptual Physics - Hewitt


Electromagnetism - Grant, Phillips