Impedance, Part 1

October 5, 2013 in AV Design Tips, The Basics by Sam Davisson

Resistance / ImpedancePart 1: Transmission Line (Characteristic) Impedance

Impedance has been the most requested subject since I started the “Basic’s” series. So I thought it about time to address it. Problem is, no one actually mentioned what area of impedance they were confused about and was looking for clarification on. Perhaps some are wondering why when you measure across the center conductor and braid of a 75ohm coax cable you don’t read 75ohms. Or how in the world you would ever know if a connector was a 75ohm connector or one of the 50ohm variety? Does all that mumbo jumbo have anything to do with audio amplifiers and the speaker connected to it.

Every signal input, and every output, has an impedance, this "impedance" represents the relationship between voltage and current which a device is capable of accepting or delivering. Electricity is all about the flow of electrons in wire. "Voltage" is a measure of how hard the electrons are pressing to get through, it’s like water pressure in a pipe. "Current," measured in amps, is a measure of the rate at which the electrons are flowing. It’s like the gallons-per-minute flow in a pipe. Total power delivery, in an electrical circuit, is measured in watts, which are simply the volts multiplied by the amps. A number of watts may represent a very high voltage with relatively low current (such as we see in high-tension power lines) or a low voltage with very high current (such as we see when a 12-volt car battery delivers hundreds of amps into a starter).

An output circuit can’t supply just any combination of voltage and current we want. Instead, it’s designed to deliver a signal into a specific kind of load ("load," here, simply meaning the device, such as the TV input that the signal is being delivered to). The "impedance" of the load represents the opposition to current flow which the load presents.

The impedance of the load is expressed in ohms, and the relationship between the current and the voltage in the circuit is controlled by the impedance in the circuit. When a signal source sees a very low-impedance circuit, it produces a larger than intended current; when it sees a very high-impedance circuit, it produces a smaller current than intended. These mismatched impedance’s redistribute the power in the circuit so that less of it is delivered to the load than the circuit was designed for, because the nature of the circuit is that it can’t simply readjust the voltage to deliver the same power regardless of the rate of current flow. What happens in an impedance mismatch between a source and load; power isn’t being transferred properly because the source circuit wasn’t designed to drive the kind of load it’s connected to. In some electronic applications, this will burn out equipment. A radio transmitter must be able to deliver its power into an antenna load that presents the proper impedance or it will self-destruct, and an audio amplifier can possibly be destroyed by attaching it to speakers of the wrong impedance.

Hopefully that is a rare occurrence. So why do we really care about impedance mismatches? The reason is that when impedances are mismatched, the mismatch causes portions of the signal to reflect. This can happen at the source, at the connectors, at any point along the cable, or at the load and when a portion of the signal bounces backward down the line, it combines with and interferes with the portions of the signal that follow it. This is why, in the case of a impedance mismatch your audio quality suffers. With digital video these reflections can cause a "sparkle" effect in your picture or a complete loss of picture.

So, when I say that the input impedance of HD SDI input jack is 75 ohms, that’s what I mean. But what does it mean to say that the impedance of the cable between the source and display is 75 ohms?

Well, first, it doesn’t mean that the cable itself presents a 75 ohm load. If it did, the total load would now be 150 ohms, and you’d have an impedance mismatch. Furthermore, if the cable itself constituted a 75 ohm load, that load would be dependent on length. So a cable twice as long would be 150 ohms, a cable half as long would be 37.5 ohms, and so on. In case it’s not obvious by now, another thing that it doesn’t mean is that the resistance of the cable will be 75 ohms. Resistance, which also confusingly happens to be measured in ohms, has nothing to do with characteristic impedance, which can’t be measured by using a VOM.

When I say that the characteristic impedance of a cable is 75ohms, or 50, 110, 300, or what-have-you, what I mean is that if we attach a load of the specified impedance to the other end of the cable, it will look like a load of that impedance regardless of the length of the cable. The object of a 75 ohm cable is simply to "carry" that 75 ohm impedance from point A to point B, so that as far as the devices are concerned, they’re right next to one another. If we take a hundred feet of 300-ohm television twin-lead cable, solder it to RCA connectors, and stick that in between the display and an an analog device, the load, as "seen" by the analog device, will not be 75 ohms. How bad the mismatch is, and what the consequences of it are, will depend on a variety of factors, but it’s fair to say that this sort of mismatch needs to be avoided.

Transmission line impedance is critical in some applications, and not so critical in others. In analog (line level) audio, impedance has become a non-factor as designers of these circuits dispensed with the idea of matched impedance’s completely and use what is called voltage matching instead.

The idea here is to engineer the equipment to have the lowest possible output impedance and a relatively high input impedance. The difference between them must be at least a factor of ten, and is often much more. Modern equipment typically employs output impedance’s of around 150ohms or below, with input impedance’s of at least 10kohms or above. With the minuscule output impedance and relatively high input impedance, the full output voltage should be developed across the input impedance.

Relatively high-impedance inputs such as these are called bridging inputs. They have the advantage that several devices can be connected in parallel without decreasing the impedance to any significant degree. The voltage developed across each input remains high and the source does not need to supply a high current. As an example, a mixing console output is feeding two tape machines. Each machine now has an input impedance of 30kohms. Connecting two in parallel will only reduce the combined input impedance to 15kohms, which is still substantially higher than the 150ohm output impedance of the console. Therefore the input voltage will be virtually unaffected. I calculate a loss of 0.04dB. Even connecting a third device to the output, the impedance would only fall to 10kohms and the level would fall by a further 0.05dB, which would not be audible. Because bridging inputs make studio work much easier, the idea of voltage matching is now employed universally in line-level audio equipment, irrespective of the actual reference signal levels used.

Back on topic now, the behavior of cables changes as signal frequencies increase. This is so because as frequency increases, the electrical "wavelength" of a signal becomes shorter and shorter. As the length of a cable becomes closer to a large fraction of the electrical wavelength of the signal it carries, the likelihood of significant reflections from impedance mismatch increases. The whole cable can resonate at the wavelength of the signal, or of a portion of the signal, and the impact on signal quality will be anything but good. Many signals are complex, occupying not a single frequency, but a whole range of frequencies. This is why we so often speak of the "bandwidth" of a signal, and so a mismatch will affect different parts of the signal differently.

Because the effects of impedance mismatch are dependent upon frequency, the issue has particular relevance for digital signals. Where analog audio or video signals consist of electrical waves which rise or fall continuously through a range, digital signals are very different. They switch rapidly between two states representing bits, 1 and 0. This switching creates something close to what we call a "square wave,", a waveform which, instead of being sloped like a sine wave, has sharp, sudden transitions. Although a digital signal can be said to have a "frequency" at the rate at which it switches, electrically, a square wave of a given frequency is equivalent to a sine wave at that frequency accompanied by an infinite series of harmonics, that is, multiples of the frequency. If all of these harmonics aren’t faithfully carried through the cable and, in fact, it’s physically impossible to carry all of them faithfully, then the "shoulders" of the digital square wave begin to round off. The more the wave becomes rounded, the higher the possibility of bit errors becomes. The device at the load end will, of course, reconstitute the digital information from this somewhat rounded wave, but as the rounding becomes worse and worse, eventually there comes a point where the errors are too severe to be corrected, and the signal can no longer be reconstituted. The best defense against the problem is, of course, a cable of the right impedance: for digital video or SPDIF digital audio, this means a 75 ohm cable like Belden 1694A; for AES/EBU balanced digital audio, this means a 110 ohm cable like Belden 1800F.

Fortunately, for most applications, it’s very easy to choose the right impedance cable. All common analog video standards and HD SDI use 75ohm cable, as do coaxial (unbalanced) digital audio connections. If you have balanced AES/EBU type digital audio lines, you’ll want 110 ohm AES/EBU cable. There are a few others you may bump into, however, and it’s good to be aware of them. RG-58 coax, such as is often used for CB or ham radio antenna lines and CATV, is 50 ohms, not suitable for video use. Twin-lead cable, the two wires separated by a band of insulation that used to be the most common way to hook up a TV antenna is a 300 ohm balanced line.

Connectors have impedance, too, and should be matched to the cable and equipment. Many BNC connectors, especially on older cables, are 50ohm types, and so it’s important to be sure that you’re using 75 ohm BNCs when connecting video lines. RCA connectors can’t quite meet the 75 ohm impedance standard because their physical dimensions just aren’t fully compatible with it, but there are RCA plugs which are designed for the best possible impedance match with 75 ohm cable and equipment.

Coming Impedance Part II, Speakers, Amplifiers and Nominal Impedance

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