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Testing Todd: Why TDR?

Time-domain reflectometry (TDR) is a measurement of impedance in a transmission line. This becomes very important in high speed or RF printed circuits. As a long-time amateur radio operator, I have had a lot of experience with characteristic impedance regarding power transmission.

For example, this is very important with transmission lines leading to an antenna. In the circuit board world, this could be cellphones or Wi-Fi devices. These devices transmit and receive RF signals at high frequencies, and mismatches from the transmission line to the antenna can have adverse effects on performance. So, in amateur radio, standard transmission cables are used with known impedance values. One example is coaxial cables, such as RG-8 or RG-58. These cables have a characteristic impedance of 50 ohms. This is considered a “constant” so that changes to only the antenna affect the resonance of the output.

In RF applications, a mismatch of the antenna length at the desired frequency can have significant effects on the effective radiated power (ERP) or reception functionality. When this happens there is a change in the standing wave ratio (SWR). On a matched transmission line to load (antenna), the SWR will be extremely low, and a perfect match will be a ratio of 1:1. This means full transmitted power is being radiated or passed to the load. As SWR increases, a portion of the power of the circuit is reflected toward the source or transmitting circuit. The higher the SWR, the more power is reflected. This is dangerous to the source as heat is produced and the high reflected signal can damage the output circuit causing failure.

Let’s look at a Wi-Fi router. It is typically transmitting in the 2.4 GHz–5 GHz bands. These routers usually only transmit milliwatts, so it is very important that the best ERP can be achieved (yes, there are antennas in these devices). Depending on the design of the router, the length of the antenna may vary. Since we are in such a high frequency, the antenna will be small. For example, it’s not a coincidence that router antennas are only about 4-5" long. That is a full wave at 2.4 GHz (936/f = length of full wave in feet, where f is frequency). At 2.4 GHz, it’s actually 4.68". As the frequency increases, the actual antenna length requirement shortens. As the 2.4 GHz band is 2.401–2.484 GHz, the manufacturers will target a mean resonance at the middle of the band, 2.445 GHz. That is roughly 4.58". You can double check by measuring the length of your router antenna(s).

In our router example, these typically transmit between 10-25 milliwatts. Matching the transmission line to the antenna is critical so as to radiate as much of the signal as possible. As SWR increases due to mismatch, the ERP of that 10–25 milliwatts is degraded. We start having loss on the circuit. When we talk about signal gain and loss, we use decibels (dB). When we start reflecting power back, we are losing ERP. Just for reference, a 3 dB loss is half the transmitted power, so, if we have a 3 dB loss when transmitting 10 milliwatts, we are now only effectively radiating 5 milliwatts. That’s not good when we are using such low power to begin with.

But, you say, my router has 5 GHz capability, too, and your calculation was only for 2.4 GHz. Why use the same antenna? The beauty of radio waves is they can work harmonically, or more specifically, using multiples of themselves. The Wi-Fi 5 GHz band is not just by accident. The 5 GHz band is a close harmonic of the 2.4 GHz band. So, using the same antenna at 1 full wave for 2.4 GHz, they can obtain matches on the 5 GHz band. A second antenna is not needed. The matching will be a little fuzzy regarding SWR but anything less than 1.5:1 is considered optimal while 2:1 is considered acceptable.

I’m sure you have noticed those huge towers on the hills rising hundreds of feet in the air. The actual transmission antennas are very small by comparison. Using our antenna calculator, I know of an FM station transmitting here in Oregon on 92.3 MHz on a tower over 1,000 feet in elevation. However, the driven element for a full wave is only 10 feet, 3 inches. When you look at these giant towers, remember the giant footprint is just to elevate the antennas as high above the ground as possible to propagate the transmitted wave as far as possible.

Okay, we now understand the significance of matching transmission lines to loads (antennae). In the finished circuit board, we have many other variables: ICs, capacitors, inductors, and resistors. Again, the transmission lines (traces) running around on the board need to be constant regarding calculating responses to signals. Mismatching can cause changes in waveforms that may not be desirable. Here, inductive and capacitive reactance can manipulate frequency waveforms, which may be desirable if designed. However, a mismatched transmission line can skew those waveforms, resulting in undesirable results. If the circuit becomes more inductive, the voltage waveform will lead the current waveform by 90 degrees. Conversely, when the circuit becomes more capacitive, the current waveform will lead the voltage by 90 degrees. Using these electrical properties, circuits can provide either gain or attenuation. However, this is only successfully achieved by stable transmission lines as a constant.

So, now we know why TDR can be very important in circuit design. Matched transmission lines provide optimal circuit performance, while mismatched lines can provide high reflected waves, signal loss, and even transmitting element failure.

This column originally appeared in the September 2023 issue of PCB007 Magazine.