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How do I check my SWR?
Checking SWR with radios that have an SWR CAL knob

CAL Switch: Flip the SRF/SWR/CAL switch to CAL This changes what your radio's meter is going to tell you. Right now, we want it to tell us where the SWR meter is calibrated.
SWR CAL Knob: Turn your radio to channel 20. Key your microphone and turn the SWR CAL knob until the needle on your radio's meter goes to the CAL mark on the top right of the meter. Unkey the mic when adjusted.
SWR Switch: Now you've calibrated your meter. The next step is to get the reading. Flip your SRF/SWR/CAL switch to SWR.
Get your reading: Key your microphone. Look at the bar or line marked SWR. On many radios, this is the top line. You should see the following numbers on the SWR line of your meter: 1, a space for 1.5, 2, and 3. If your SWR reading is below the 2 mark, your reading is within tolerance. If your SWR reading is below the 1.5 notch, your antenna system is working very well. If the reading is almost or exactly a 1, then your system is working as good as it can.
Checking SWR with radios that have built-in automatic SWR calibration (this is your radio if you have an SWR meter, but do not have an SWR CAL knob, a very helpful feature). Unsure which you have, do your own reseach to find out!

SWR Switch: Your radio should have a button or a switch that says "SWR". Turn this on now. Start with channel 20.
Get your reading: Key your microphone. Look at the bar or line marked SWR. On many radios, this is the top line. You should see the following numbers on the SWR line of your meter: 1, a space for 1.5, 2, and 3. If your SWR reading is below the 2 mark, your reading is within tolerance. If your SWR reading is below the 1.5 notch, your antenna system is working very well. If the reading is almost or exactly a 1, then your system is working as good as it can.
How does tuning my SWR affect my radio?
It's important to note, contrary to popular opinion, your SWR does not affect your squelch. Instead, tuning your antenna system to your vehicle directly affects the peak performance of your CB system. When we talk about swr meter tuning, really what we mean is making your antenna work on the channels (frequencies) you're operating on. If your antenna is not tuned correctly, your radio's peak performance will suffer and you run the risk of damaging your radio. Proper SWR tuning is vital to the health and performance of your radio system!

What is Standing Wave Ratio (SWR) anyhow?
SWR is a reflection of the impedence matching in your antenna system. The SWR Meter really measures impedence, which in simple terms, is the measurement how efficiently your signal can pass through your antenna system. If you have an impedence mismatch, some amount of your radiated signal will not be able to pass through your antenna system. Instead, part of it will get reflected back to your transceiver. When this ocurrs, an amount of your potential output isn't radiated away from your antenna and instead travels back along your system creating standing waves.

Now what do I do with this SWR number?
The answer depends on what your meter reading was, and what you are doing with your CB radio. If your reading was less than a 2, and you mainly use your CB for casual use, then you are done. Congrats! There is nothing else you need to do. However, if your SWR reading was above a 2, or if you want to talk on a different channel (or channels) or if you want to optimize your system for the best peak performance, keep reading.

How do I tune my antenna now that I have my SWR reading?
The process can be summed up like this. 1. Check your SWR reading. 2. Adjust something on your antenna. 3. Re-check your SWR to verify your adjustments. Here's a step by step process for setting or tuning the SWR on your CB antenna:

Check your SWR meter : Write down the SWR reading on channels 1, 20, and 40 based on the instructions above.
Adjust your antenna: If your SWR reading is higher on channel 40 than it is on channel 1, lower something on your antenna. If channel 1 is higher than 40, raise something on your antenna. If channels 1 and 40 are (about) the same, and your lowest reading is on channel 20, then you are done.
Verify your SWR: In most cases you're looking for the same SWR reading on channels 1 and 40, with your lowest on 20. As long as your SWR is less than a 2 on all 40 channels, you're good.
What about dual antennas?: The process is the same, just adjust both antennas at the same amount.
Impedence in most CB systems
Your CB radio, antenna, and cable are all rated at 50 ohms. This reading is reflected in your SWR meter. If you're using a co-phase, or dual antenna system, the coax cable is rated at 75 ohms per side. When two 75 OHM cables meet, the impedence becomes 50, thus allowing your two antennas to actually act as a 50 ohm system - which is what your antenna and radio are designed for.

Additional Research Source
Helpful websites such as Wikipedia, Firestik and the ARRL.org are all great tools to use when trying to learn more about SWR. Find an article you need, and they can point you in the right direction. In radio engineering and telecommunications, standing wave ratio is a measure of impedance matching of loads to the characteristic impedance of a transmission line or waveguide. Impedance mismatches result in standing waves along the transmission line, and SWR is defined as the ratio of the partial standing wave's amplitude at an antinode to the amplitude at a node along the line. The SWR is usually thought of in terms of the maximum and minimum AC voltages along the transmission line, thus called the voltage standing wave ratio or VSWR. For example, the VSWR value 1.2:1 denotes an AC voltage due to standing waves along the transmission line reaching a peak value 1.2 times that of the minimum AC voltage along that line. The SWR can as well be defined as the ratio of the maximum amplitude to minimum amplitude of the transmission line's currents, electric field strength, or the magnetic field strength. Neglecting transmission line loss, these ratios are identical. The power standing wave ratio is defined as the square of the VSWR, however this terminology has no physical relation to actual powers involved in transmission. Wikipedia

Tuning your CB Radio
A common misconception with SWR tuning is that you are tuning your radio, or tuning your antenna to your radio. This isn't what's happening at all, rather, you are tuning your antenna to the vehicle on which it's mounted. Once you've set your SWR, changing radios will NOT affect your readings. You do not tune your antenna to your CB! Additional research on radio and antenna tuning can be found on wikipedia.