# Wave resistance 50 or 75 Ohm, copper iron or copper?

There is a persistent prejudice and, one might even say, delusion of many people relatively high frequency cables. As an antenna design and production company, we are constantly being asked this question. I will try once and for all to put an end to this issue and close the topic of using 75 Ohm cables instead of 50 Ohm for the purpose of transmitting signals of low power. I will try not to bother the reader with complex terms with formulas, although some minimum of mathematics is still necessary to understand the question.

In low frequency radio engineering to transmit a signal with the specified parameters of the current-voltage conductor is needed, which has some properties of isolation from the environment and linear resistance, so that at the point of reception of the low-frequency signal we have received sufficient for subsequent processing of the signal. In other words, any conductor has resistance, and it is desirable that this resistance is as small as possible. This is a simple condition for low-frequency technology. For signals with low transmitted power, a thin wire is enough for us, for signals with high power, we must choose a thicker wire.

In contrast to low-frequency radio engineering, high-frequency engineering has to take into account many other parameters. Undoubtedly, as in low-frequency technology, we are interested in the power transmitted by the transmission medium and resistance. The fact that at low frequencies we usually call the resistance of the transmission lines at high frequencies are called losses. At a low frequency, the losses are primarily determined by the transmission line's own linear resistance, while the so-called Skin effect appears on the RF. Skin effect-leads to the fact that the current displaced by the high-frequency magnetic field flows only on the surface of the conductor, or rather in its thin surface layer. Because of what the effective cross-section of the conductor can be said to be reduced. I.e. under the same conditions for pumping the same power at low frequency and high require wires of different cross sections. The thickness of the skin layer depends on the frequency, with increasing frequency the thickness of the skin layer decreases, which leads to losses greater than at lower frequencies. The skin effect is present at an alternating current of any frequency. For clarity, I will give some examples.

So for the current frequency of 60 Hertz, the thickness of the skin layer is 8.5 mm. and for the current of 10 MHz, the thickness of the skin layer is only 0.02 mm. is not it a striking difference? And for frequencies of 100, 1000 or 2000 MHz, the thickness of the conductive layer will be even less! Without going into mathematics, I will say that the thickness of the skin layer depends primarily on the conductivity of the conductor and frequency. Therefore, to transfer the maximum power to the RF, we need to take the cable with the largest surface area of the Central core. At the same time, given that the microwave thickness of the skin layer is small, we do not necessarily use a solid copper cable. The differences from using a cable with a steel center conductor covered with a thin layer of copper you probably won't even notice. Unless it will be more rigid on a bend. Of course, it is desirable to have a thicker layer of copper on the steel conductor. The use of a solid copper cable has, of course, advantages, it is more flexible, it can transmit more power at lower frequencies. Also, the coaxial cable is often used to transmit the DC supply voltage of the preamplifiers, and then the copper cable is also out of competition. But for the transfer of small capacity of no more than 10-200 mW to microwave from an economic point of view, it is more justified to use copper-plated cable. We assume that the issue of choice between copper and copper cables closed.

To understand the difference between cables in the wave resistance, I will not tell you what the wave resistance of the cable. Oddly enough, it is not necessary to understand the difference. First, let's understand why there are cables with different wave resistances. First of all, it is connected with the history of radio engineering. At the dawn of radio engineering the choice of insulating materials for coaxial cables was very limited. It is now we normally perceive the presence of a huge number of plastics, foamed dielectrics, rubber with the properties of conductors or ceramics. 80 years ago, none of this happened. There was rubber, polyethylene, paraffin, bakelite, in the 30s invented Teflon. The wave resistance of cables is determined by the ratio of the diameters of the Central inner conductor and the outer diameter of the cable.

Below is the nomogram.

The thickness of the сentral conductor is determined by its ability to pass the greatest power. The outer diameter is selected depending on the filler dielectric used between the two conductors. Using the nomogram, it becomes clear that the range for the industrial manufacture of wave resistance of the cables is in the range of 25 – 100 Ohm.

So, one of the criteria – manufacturability. The next criterion is the maximum transmitted power. Omitting mathematics will report that to transmit the maximum power using the most common dielectrics optimal wave resistance in the range of 20-30 Ohm. At the same time, the minimum attenuation corresponds to the wave resistance of 50-75 Ohm. Moreover, cables with a wave resistance of 75 Ohm have less attenuation than cables with a wave resistance of 50 Ohm. It becomes more or less clear that it is more profitable to use 75 Ohm cable for low power transmission, and 50 Ohm cable for high power transmission.

Now I think it is necessary to consider the less important issue of the coordination of the transmission line. I'll just try to answer the questions about whether it is possible to connect 75 Ohm cable instead of 50 Ohm.

Understanding the issues of coordination requires special knowledge in radio engineering. Therefore, we will limit ourselves to stating the facts. And the facts are that for the transmission of the signal with the least losses, the internal resistance of the signal source must be equal to the wave resistance of the cable. At the same time, the wave resistance of the cable should be equal to the wave resistance of the load. In other words, the source of the signal is the transmitter, the load is the antenna. Let's analyze several situations in which to simplify the cable will be considered ideal without loss, and transmitted through the cable power is small - up to 100-200 milliwatts (20 dBm).

Consider a situation where the output impedance of the transmitter 50 Ohm, we connect to it 50 Ohm cable and 75 Ohm antenna. In this case, the loss will be 4% of the output power. Is it much? The answer is ambiguous. The fact that HF radio operate mostly logarithmic values, converted to dB. And if 4% is converted to decibels, the losses in the line will be only 0.18 dB.

If we connect the transmitter with 50 Ohm output to the 75 Ohm cable and then to the 50 Ohm antenna. In this case, 8% of the power is lost. But bringing this value to decibels, it turns out that the loss will be only 0.36 dB.

Now consider the typical attenuation of cables for the frequency of 2000 MHz. And compare what is better to use: 20 feet of 75 Ohm cable or 20 metres of cable of 50 Ohm.

Attenuation at 20 metres for a famous expensive brand Radiolab cable 5D-FB is 0.3*20= 6 dB.

Attenuation at 20 meters for high-quality Cavel cable SAT703 is 0.29*20= 5,8 dB.

Now let's compare prices. 20 meters of cable Radiolab 5D-FB are at best around 80*20=1600 RUB At the same time 20 meters of cable SAT703 Cavel is 25*20=500. the Difference in the price of 1100 RUB quite noticeable. The advantages of 75 Ohm cables include the ease of cutting, the availability of connectors. So if someone once again starts to be clever and tell you that for 3G modem well, you can not use 75 Ohm cable, then with a clear conscience send it....to… or to me for our wonderful antennas. Thank you for listening.