How can we maximize power from the transceiver out through the antenna?
Somehow, match the impedances at the transceiver and the antenna.
That sounds simple enough, but let’s dive deeper.
The Maximum Power-Transfer Theorem states that to transfer the maximum amount of power from a source to a load, the load impedance must match the source impedance. But in the case of amateur radio its not quite that simple. We also have to account for the possibility that the feed line between the radio and the antenna has a characteristic impedance, and if it happens to have a length greater than 1/8th of a wavelength of the operating frequency then the feed line itself becomes an important consideration in the overall calculation.
If the impedances aren’t matched, maximum power will not be delivered and standing waves will develop along the feed line. Some of that power gets reflected back toward the source. The amount of power lost due to reflection is a function of the reflection coefficient and the standing wave ratio. The greater the impedance mismatch, the larger the losses.
In amateur radio it is often said that an SWR less than 2 is adequate. An SWR of 2 means that reflected power is 10%. Therefore, 90% of the power is reaching the load where it has a chance of being radiated. Add to this the fact that the feed line introduces some loss measured in decibels per foot. So the longer the feed line the greater the loss. There is a two edged sword in all of this. If the source and load are well matched the feed line length will be insignificant. But the worse the match, the source will see a complex impedance that is a function of the feed line length. In short, impedance matching is important.
How can we match Impedance?
Basic electronics theory tells us there are two possible ways to go, but only one of them is helpful for our purposes
- Resistive matching is cheap and frequency insensitive, but dissipates power. That won’t help us.
- Reactive matching is power efficient but it is frequency sensitive. This will work, but we have to plan ahead.
To understand this idea of impedance matching a bit better, let’s consider a common device – the transformer, and see how it works. A transformer is, in simple terms, an impedance matching device. On one side it has a particular ratio of voltage to current. On the other side it has a different ratio of voltage to current. Remember Ohms Law?
Zsec = the number of turns in the secondary winding
Zpri = the number of turns in the primary winding
Use the formula below to find the sqrt of the Z ratio
Zsec / Zpri = n2
If n = 2, Z ratio = 4; If n = 3, Z ratio = 9; etc
So suppose an antenna with a 450 Ohm impedance is connected on the secondary winding side. Our transceiver with a 50 Ohm impedance is connected on the primary winding side. If Zsec = 9 turns, and Zpri = 3 turns, then the ratio is 3 to 1. The n squared value is 9. The antenna impedance of 450 Ohms, divided by 9, is 50 Ohms, which is what the transceiver wants to see. This transformer looks like it would be an excellent choice to transfer maximum power.
Here are a couple more formulas we should think about. When we build a transformer we are not only affecting resistance. We are changing the relationships of voltage and current as well. We have to plan for this too when we are selecting components to build our transformer, feed line, antenna, etc.
(voltage out) = ((turns ratio) x (voltage in))
(current out) = ((current in) / (turns ratio))