# Lesson 9 - Impedance versus Resistance

## What is Impedance?

If you have gotten that far, you must remember that resistance is the opposition to the flow of current. More specifically, resistance is the opposition to the flow of Direct Current (DC). DC is current that flows steadily in one direction, as opposed to AC current which alternates between positive and negative values.

Note: there is a particular case of current that fluctuates in intensity but always flows in one direction. In most cases, this can be treated as the sum of a DC current that has the average value of the fluctuating current and an AC current equal to the alternating part. So the effects of the DC part will be evaluated as if the DC was by itself, and we will do the same for the AC part. This is not always true, but it will be close enough for now.

For the rest of this lesson, when I refer to AC current, I mean true AC current that has no DC component.

Impedance is the opposition to the flow of AC current. If we consider DC to be a particular case of AC (it's AC where the frequency is zero), then we can consider Resistance to be a particular case of Impedance (Impedance at Frequency zero).

Resistance is easy to measure with an ohm-meter. Impedance is more difficult because you need a source of AC, and you need to be able to measure AC voltage and current. In addition, AC can be any frequency, from DC to daylight, so when you talk about impedance, you must make sure that the frequency or frequencies of interest are indicated.

For instance, saying that such or such device has 50 ohm impedance may not mean a lot if you do not specify the frequency or the bandwidth where this is measured.

In many cases, the bandwidth will be implied. For instance, if coaxial cable is specified to have 50 ohm impedance, the cable specification will also include a useable frequency range over which the impedance value will apply.

Here is a simple circuit that will illustrate the impedance of an inductor:

In this circuit, I have added a 1 milli-Henry (mH) inductor in series with the load resistance. At DC, the effect of the inductor is negligible (in real life, the inductor would add its small DC resistance to the equation, but inductance has no effect at DC (Note 1)..)

So at DC, the output voltage is actually half the input voltage:

## V(output) = V(source) * R1 / (R1 + R2)

In this case, since R1 and R2 are both 50 ohms,

## V(output) = V(source) * 50 / (50 + 50) = V(source) / 2

In the AC domain, we can no longer neglect the inductor. The inductor offers an impedance due the passage of AC currents, which is equivalent to the resistance for DC currents.

The impedance of an inductor is

## Z = L * 2 * Pi * F

Where Z is the impedance in ohm, L is the inductance in Henry, PI is 3.141592654... and F is the frequency in Hertz.

So in the AC world, the output voltage as a function of the input voltage becomes:

## V(output) = V(source) * (R1 + Z(L1) / (R1 + R2 + Z(L1))

And here is the AC Analysis response:

<Impedance-2.png>

You can see that at the lower frequency (1 kHz), the gain of the circuit is -6 dB. That means the output voltage is half of the input voltage. This is an effect of the 50 ohm impedance of the source (R2) driving the resistive part of the load (R1) which is also 50 ohm, so the voltage is in effect divided by 2.

As the frequency increases, the impedance of the inductor becomes more important and the divider ratio is no longer 2, but smaller, asymptotically 0 dB, or a gain of one.