# Transmission line

I'm currently testing a design, and using two small wires to connect an oscillator with a frequency counter (both are small circuits I have build).

So here is a question, when designing RF and connecting different circuits, when is something to be considered a transmission line?

I mean, when do I have to think about transmission line impedance matching (and to start worrying about reflection and ect.).

An interconnection should be considered a transmission line if reflections are detrimental to your application. As Leon Heller says, 1/10th wavelength is a good rule-of-thumb.

However, all this depends on the nature of the signal (1/10th of what wavelength?). With sine waves, the wavelength in the cable will be about $\frac{2 X 10^8}{f}$ where f is the frequency, but will vary according to the cable type. The effect of reflections on sine waves is to cause standing waves, so the amplitude will vary along the length of the cable but will always be sinusoidal. With square waves the situation is complicated by harmonics. Although the square-wave may have a low fundamental frequency, the harmonics introduced by the edges will be significant. The effect of reflections in this case is undershoot, overshoot or ringing depending on where the mismatches are (if both $R_S$ & $R_L$ are lower than $Z_0$ for example, you will get ringing).

So do you need to match the source? No. As long as the load is perfectly matched, the wavefront will travel down the transmission line and be fully absorbed by the load. Consider a digital system with 3.3V logic for example. If you terminated both source and load you would only get 1.65V swing at the load. Terminating only at the load is termed parallel termination.

There is also a technique known as series termination in which the source is terminated but the load is left open circuit. In this case, a half-amplitude edge propagates down the line and is reflected back to the source, lifting the voltage to full amplitude as it returns until it is absorbed by the source termination. Along the line, you would see a 'stepped' signal except right at the load where you would see a clean waveform.

• I will try some simulations in spice, to see how this works. Ok, so basically the source impedance matching is only important for maximum power transfer? (If source is 10 ohms, and the cable and load is 50 ohms, I will not get maximum power transfered to the load). – JakobJ Apr 13 '11 at 7:15
• That depends on what you can vary. If the source impedance is fixed at 10 Ohms, you would get maximum power transfer with a 10 Ohm cable and load. If both the cable and load are fixed at 50 Ohms, you would get maximum power transfer with a source impedance of zero. If the source is fixed at 10 Ohms and the cable is fixed at 50 Ohms, you could get maximum power transfer with a 10 Ohm load but only if the cable length is an odd multiple of half-wavelengths ($\frac{\lambda}{2}$, $\frac{3\lambda}{2}$ etc) but this would only be appropriate with sine waves or a narrow-band signal. – MikeJ-UK Apr 13 '11 at 9:41
• It is possible to match any impedance at a specific frequency by adding capacitance/inductance at the source see antenna tuning or lengths of transmission line see stub matching. – MikeJ-UK Apr 13 '11 at 9:43

As a rule, a transmission line isn't required if the length of the connection is under 1/10 of a wavelength.

A low-impedance source can generally drive a high-impedance load without any problems. Loss of signal results if they are the other way round, and a buffer stage is usually the answer.

Impedances should be matched when using transmission lines.

• Hi, thank you very much for your answer. A second question, if the line is longer than 1/10, and I use a transmission line. Do I always have to match the source output impedance (with the line impedance)? even if the connection from the source to the beginning of the transmission line is short? – JakobJ Apr 12 '11 at 12:45
• Okay, so I will not get a reflection from the beginning of the transmission line, if the source output impedance is not matched? – JakobJ Apr 12 '11 at 13:11
• No, the impedance should be matched. – Leon Heller Apr 12 '11 at 13:13
• A very big rule people forget is to treated the line as a lumped LC circuit if it is below 1/10 the wavelength. The inductance and capacitance of the line can still cause substantial ringing. – Kortuk Apr 12 '11 at 13:53
• @JakobJ, if your source impedance does not match your line impedance your wave will not be full magnitude as it travels the line. – Kortuk Apr 12 '11 at 14:11

Every line is a transmission line, however different situations require different level of rigour.

At low frequencies - from DC to few hundred MHz, short transmission lines have only very small inductance and capacitance and can be usually ignored because they don't contribute much to input of output impedance of what they are connecting. The situation with them is similar to the case when the stages are connected directly. Once you start moving into GHz range, impedance of the line becomes significant and you have to treat it as separate stage of your device and match it. When the line is long, like in the case of cable, impedance also goes up and becomes significant, and you have to match it.

At high power levels reflected wave can destroy previous stage and you have to care about matching even at low frequencies. For example if you try to transmit 100W with disconnected antenna, you are likely going to fry your power amplifier (unless it has protection against such situation).

Example: short PCB trace is going to have say 10 nH inductance, which at 10 MHz would give it reactance 0.63 ohm (open circuit), shunt capacitance 1 pF, or capacitive reactance 15783 ohm (high impedance), and resistance under 1 ohm - all values insignificant if the input and output impedance of the stages is 50 ohm. At 2 GHz it would be reactance 125 ohm and shunt capacitance 79.6 ohm - significant values that would require redesign into transmission line.