Lesson 29

Effective Radiated Power

In an earlier lesson we discussed “link margin.” It was where you calculate the additions and losses to signal in your antenna network. Another way to look at that is a term called effective radiated power. This is a view of the full station output, taking into account all gains and losses. Effective radiated power is typically abbreviated as ERP. How is link margin different from ERP? With ERP you’re calculating the expected watts out of your antenna. 

Several questions on the exam ask you to calculate the effective radiated power given several parameters. The formula to get ERP goes like this:
ERP equals Transmitter Power in Watts times 10 to the power of Gains divided by 10. 

ERP = TxWatts * (10Gains/10)

It’s easy when you walk through it. Here’s the question we’ll work through.
What is the effective radiated power (ERP) of a repeater station with 150 watts transmitter power output, 2 dB feed line loss, 2.2 dB duplexer loss, and 7 dBd antenna gain?

We’ll start like we did with link margin. Sum out gains and losses. We’ll hold off on using the transmitter power output for now.  In this question it’s  7 dB of antenna gain, minus 2 dB of feedline loss, minus 2.2 dB of duplexer loss equals a net gain of 2.8 dB.    Let’s put that in for “Gains” and calculate the parenthesis.  

ERP = TxWatts * (102.8/10)

2.8 divided by 10 is easy, just move the decimal point one place, so we have 0.28. Now put the 150 watts in the formula and finish the math.

ERP = 150 watts * 100.28

150 watts times 10 to the 0.28 power equals 286 watts rounded. 

ERP = ~286 watts

Here’s another question that asks you to calculate ERP. What is the effective radiated power (ERP) of a repeater station with 200 watts transmitter power output, 4 dB feed line loss, 3.2 dB duplexer loss, 0.8 dB circulator loss, and 10 dBd antenna gain?

Let’s start by calculating the total gain, which is very easy. 10 dB gain minus 4 dB, minus 3.2 dB, minus 0.8 dB leaves us with an overall gain of 2 dB.

Now we just need to plug our numbers into the ERP formula.

ERP = TxWatts * (102/10)

2 divided by 10 is 0.2. So we can bring in the 200 watts of transmitter power and solve.

ERP = 200 watts * 100.2

We arrive at 200 watts times 10 to the 0.2 power equals 317 watts rounded.

ERP = ~317 watts

Are you getting the hang of ERP calculations? There’s one more to do for the exam. Now we have a repeater station. It has 200 watts transmitter output, 2 dB feed line loss, 2.8 dB duplexer loss, 1.2 dB circulator loss, and 7 dBi antenna gain.

First we’ll calculate the total gain again: 7 dB minus 2 dB minus 2.8 dB minus 1.2 dB gives us a net gain of 1 dB.  Here’s that 1 dB in the formula. 

ERP = TxWatts * (101/10)

Let’s finish the math. ERP equals 200 watts times 10 to the 0.1 power equals 252 watts rounded. 

ERP = 200 * (100.1)

ERP = ~252 watts

Frequency does have an impact in some gain calculations when using reflective elements. In an ideal parabolic dish the antenna gain increases 6 dB when the operating frequency is doubled.

The Smith Chart

Students tell us that Smith Charts are intimidating, but we think this section will make it easy for you. Here’s something to remember, we cover 11 potential exam questions in this section. Only one will be on the exam you see on test day.   

So who is Smith, and what does his chart do? Philip H. Smith gave us a graphical tool. It’s used for solving problems in transmission lines and matching circuits. The Smith Chart looks complex but let’s look at it piece by piece. We’ll start by mapping resistance and reactance on this chart. Resistance and reactance are the two families of circles and arcs that make up a Smith chart.

We’ll use Figure E9-3, a simplified version of the chart, to help us.

Reactance is read on the large outer circle. This is where reactance arcs will  terminate. So, this is the reactance axis. The only straight line shown in the chart is the resistance axis.

To map resistance and reactance on the we will use two coordinate systems. Those coordinate systems are resistance circles and reactance arcs. Remember “resistance circles and reactance arcs” for a Smith Chart. If you have that you will nail these three questions!

So what transmission line metrics will we calculate using our Smith chart? First it can calculate impedance along transmission lines. In some cases impedance and SWR values in transmission lines are often determined using a Smith chart.      


Normalized impedance Smith chart

Some of the scales you see on a Smith chart are wavelength scales. They are calibrated in fractions of transmission line electrical wavelength. The arcs on a Smith chart represent points with constant reactance. Remember, reactance arcs!

A third family of circles can be added while designing impedance matching networks. Those are constant-SWR circles.

While working with a Smith chart you use a process called normalization. A Smith chart is normalized by reassigning impedance values with regard to the prime center. Impedance is the key term here. 

So when would you use a Smith chart? One common use is to determine the length and position of an impedance matching stub. 

That’s all you need to know about Smith charts for the Amateur Extra exam. 

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