Now with pictures!
I have been neglecting my blog as of late, so I decided to write at home, and take smaller chunks. Hopefully the pictures will help to visualize the concepts – it always helps me, I’m a visual type.
In the
previous installment we talked about inductors and capacitors, their reactive nature, and how to calculate their impedances. Next time we’ll talk about the voltage and current and show how the impedances affect the current that flows through a circuit. After all it’s the current through the voice coil that determines the output level of a speaker.
To start our conversation today we will use a simple series RLC circuit.
The total impedance seen by the voltage source is Z=Z(R)+Z(C)+Z(L).
I’ve picked values for the R, C, and L that will do something interesting in the area of interest – the audio band: R=10Ω, C=10μF, L=10mH. So let’s get started by doing an example at 1,000 Hz.
The impedance of a resistor is constant with frequency (at least we are going to assume it is for the time being) so Z(R1k)=10Ω.
The impedance of the capacitor is Z(C1k)=1/(2πfC)=1/(2*3.14159*1000*0.000010)=15.92Ω
The impedance of the inductor is Z(L1k)=2πfL=2*3.14159*1000*0.010=62.83Ω
We could repeat this calculation ad nauseum for every frequency, but since I have a computer…
I went ahead and used a logarithmic scale for frequency since it impossible to see much of anything on a linear frequency scale. The graph above shows the capacitive and inductive impedance for 10μF and 10mH in the audio band (plus an octave on either end). Whenever we see a curve in the graph it’s always interesting to see what would happen if we plotted the curve on a logarithmic scale.
And as expected we get straight lines. Since decibels are logarithmic we can deduce that a capacitor or inductor in the signal path will induce a linear-in- dB change in the current flowing through the circuit. But that’s a blog for another day. Just for fun, I added a curve showing the total impedance of the circuit as seen from the voltage source.
One more thing for today… Notice that the impedance of the capacitor falls exactly tenfold for every tenfold increase in frequency, and vice versa for the inductor. If all you had was a piece of log-log graph paper and knowledge of only one data point, you could draw the entire curve for any value of capacitor or inductor.