Lesson 2 : Section 2 : Reflection and transmission in log scale


Section 2: Reflection and transmission in log scale

When a port to an RF circuit is driven, some amount of energy is transmitted into the circuit, and some amount of energy is reflected back to the source. If the source impedance is perfectly matched to the load impedance (for example, a 50Ώ source to a 50Ώ load), then all of the power is transmitted from the source to the load- there is no reflection. If the load is a short (0Ώ) or an open (infinite ohms), then all of the power is reflected back to the source; in both of these cases there is no lossy resistance to burn up the power.

For a given circuit, the amount of power that is reflected (or transmitted) is related to the amount of power delivered into the system. If you put in more power, you will have more energy bouncing around in the circuit- the voltages will be higher.  Therefore, we like to describe circuits by their relative gain or loss.  We could describe an amplifier with a gain curve such as in Figure 2.2.1.  However, it is easier to simply say that this particular amplifier outputs 20 times as much power as was input- it has a power gain of 10.  We might have a voltage divider that outputs 20 times less voltage signal than was input- it has a voltage gain of 1/20, or 0.05.  

Figure 2.2.1: Power out versus power in for an amplifier with a power gain of 20

Because the amount of power transmitted or reflected is often very large or very small, rather than using a linear scale (for example, saying that the voltage gain is 0.05), a logarithmic scale is usually used. These are still ratios (comparisons between how much went out, versus how much went in), so while technically these numbers don't have units we use a mathematical unit of decibel (dB). A decibel is a unit, like a percent is a unit- it's not really a unit but it tells you that some specific math has been done to this number.  For a percent, it's a multiplication times 100.  For decibels, the relationship between the linear gain and the log gain depends on whether you have a voltage gain or a power gain.

         Equation 2.2.1

So our amplifier with a linear power gain of 20 has a logarithmic power gain of 13dBm.  Our voltage divider with the voltage gain of 0.05 has a logarithmic gain of -26dBm.