# Understanding Impedance

How To Avoid Lifeless Guitar Sounds, Digital Glitches, And Fried Amps!
Published January 2003

No home studio is immune from issues of impedance, yet the subject can seem very confusing. In this workshop we explain what the recording musician needs to know about impedance, and show you how to avoid lifeless guitar sounds, digital glitches, and fried amps!

Anyone who has read the technical specifications of any mixer, preamplifier, microphone, or pretty much any other piece of audio equipment will have come across the term impedance. Input impedance, output impedance, terminating impedance, matched impedance, and characteristic impedance are all fairly common terms in the tech specs, but what do they all mean and why are they relevant?

In this article I will try to answer these questions and to explain what you need to know about impedance in practical terms, without too much maths and science. So any electronics students reading this can stop right now and go and do their homework instead...

## What Is Impedance?

Okay, let's start with a basic definition of impedance. We should first think about electrical resistance (represented by R), measured in Ohms (symbol Ω). Imagine a simple circuit consisting of a battery and a resistor. The battery generates a voltage which tries to force a current around the circuit connected between the battery's two terminals. The resistor resists that current — the higher the value of the resistor, the lower the current will be, and vice versa. In resisting the current, a voltage difference is developed across the resistor. This important phenomenon is defined mathematically in Ohm's Law, where the battery voltage (represented by V and measured in Volts) equals the current (represented by I and measured in Amps) multiplied by the resistor's resistance value. Expressing this law algebraically, V=IR, a simple bit of algebraic rearrangement gives I=V/R. So if the battery is 12V and the resistor is 120Ω, the current flowing around the circuit will be 12V/120Ω, which is 0.1A, or 100mA.

This simple example is of a Direct Current (DC) circuit — the battery voltage is steady and unchanging (ignoring the effect of the battery losing energy over time). However, when we are dealing with audio electronics, the signal voltage changes amplitude continuously to represent the changing amplitude of the audio signal, and it alternates between positive and negative cycles. The currents that flow therefore have varying amplitudes and alternate in direction as well, and we have what is known generically as an Alternating Current (AC) circuit.

This is where things become slightly more complex, because, in addition to the resistance, there are two other fundamental components which affect the current flowing around an AC circuit. In addition to the simple resistance we have already discussed, there is also capacitance and inductance to consider. In simplistic terms these also act like resistors, except that their resistance to current changes in proportion to the frequency of the signal voltage fluctuations — the rate at which the current flowing through the circuit is made to change direction by the audio signal voltage, in this case.

All audio electronics have combinations of resistors, capacitors and inductors connected in circuits, along with 'active' components like transistors or valves which provide amplification or act as switches. To make life slightly easier for ourselves, we often consider the total 'resistance' of a complex circuit involving resistors, capacitors and inductors as a composite lump, and that's what we call the impedance.

Impedance has the symbol Z — hence references to high-Z inputs, for example — and is still measured in Ohms. However, the actual value depends to some degree on the frequency of the signal voltages involved. In audio input and output circuits the impedances are principally resistive to make interconnection easier — the impedance won't change too much over the range of audio frequencies. However, the impedance to radio frequency (RF) signals will often be very different to that at audio frequencies in order to keep RF interference out.

## Input & Output Impedances

Any device which generates a voltage has what is called an output impedance — the impedance value of its own internal circuitry as 'seen' from the outside (ie. as measured across its outputs). Similarly, any device which expects to receive a voltage input has an input impedance — the impedance 'seen' by any equipment connected to its inputs (ie. the impedance measured across the inputs). The output voltage from the source is developed across the input impedance of the destination (often called the load impedance, or simply the load), and therefore the signal voltage is passed from source to destination. However, the input and output impedances will also affect the current that flows around the circuit too.

Figure 1. Input and output impedances, also called source and load impedances.In cases where it is necessary to transfer the maximum power from a source to a destination (power being proportional to both voltage and current), the output impedance of the source and the input impedance of the destination must be equal; a situation referred to as having matched, or balanced, impedances. (Strictly speaking, the input impedance should be the conjugate of the source impedance, but I only mention this in case those pesky electronics students are still reading!) If the source and destination are physically separated by a large distance (in relation to the wavelengths of the signal frequencies being passed), then the connecting cable should also share the same impedance as both source and destination.

In a matched system like this we have the ideal power transfer arrangement, but the output voltage from the source device is shared equally across both the output and input impedances (assuming negligible cable effects). This is not a problem, as it is taken into account in the design of equipment for matched systems, but is worth bearing in mind, because it has some implications which I will return to in a moment.

 Impedance & Frequency Response The output impedance of a device and the capacitance of its connecting cable form a simple first-order low-pass filter, producing a 6dB/octave attenuation above a certain frequency. However, you need either quite a low output impedance or quite a long high-capacitance cable to bring the turnover of this filter into the audio band. Even so, it's best to select cables which have as low a capacitance as possible, and to keep cable runs as short as practicable.

## The Birth Of The 600Ω Standard

Now let's have a look at what happens if the source and destination impedances are unmatched. Well, basically, some of the energy being transferred from source to destination is reflected back from the destination (or wherever there is an impedance mismatch in the connecting circuit) towards the source — not a good thing, in general. Theoretically such reflections could manifest as echoes, or cause signals at certain frequencies to be reduced through cancellation. The telephone industry discovered the practical ramifications of impedance matching almost a hundred years ago. The wavelength of an audio-frequency signal travelling down a cable as an alternating voltage can be anything from 15000km at 20Hz to about 15km at 20kHz (wavelength reduces as signal frequency increases), so telephone cables used to carry conversations between people living in different cities can be considered to be of significant length compared to the wavelength of the signals they carry.

Since cable lengths between towns were comparable to the wavelength of the audio signals carried, it was important that the impedances of the sending and receiving telephone exchange equipment, along with the characteristic impedance of the cables (see 'Characteristic Impedance' box), were properly matched. If the impedances weren't matched correctly then reflections would occur (heard as echoes and colorations), and little energy from the source would reach the destination, resulting in faint signals coming out of the earpieces of the two telephones. These kinds of effects are rare these days, because the majority of telecoms systems are now digital — the basic problems are the same, but the technology has been developed to get around them.

In order to deal with impedance matching problems, the telecoms industry quickly standardised on a connecting impedance to ensure good transfer of audio signals with minimal reflections, and that was 600Ω. In practice, the actual telephone cables tended to have a characteristic impedance of about 140Ω, so matching transformers were employed all over the place to match between the 'standard' 600Ω, and the actual 140Ω installations.

## Matched-impedance Systems In The Studio

Figure 2. In a matched-impedance system working to the 600 ohm standard, connecting two tape machine inputs to the same console output would cause a level drop of 6dB, because each of the two parallel 600 ohm loads only receives half the signal power.The broadcasting industry, and later the recording industry, grew up directly from the technology of the telecoms industry — the VU meter being a prime example of a telecoms measurement system which has survived unchanged in the recording industry to this day. One consequence of this direct borrowing of technology was that early broadcast and recording studios also employed the 600Ω matched-impedance principle for almost everything — tape machine outputs, console inputs, and so on. However, the idea of matching impedances is not particularly relevant or practical in a recording studio, for several reasons.

For a start, we are not really interested in the transfer of power between source and destination — it's the signal voltage fluctuations which carry the information we're interested in — and it is extremely unlikely that any studio cable is going to be 15km long! For these reasons, there is no technical requirement for impedance matching. Secondly, it is common in studios to want to distribute one output signal to several device inputs (say, one mixer output to several tape recorder inputs), and there are problems with doing this within matched-impedance systems.

Consider a mixer outputting a nominal 0dBm line-up signal from a 600Ω output impedance, connected to a tape recorder input of 600Ω input impedance (see Figure 2). (For the difference between dBm and dBu, see the 'Signal Levels' box.) The tape recorder input meter will show a signal level of 0dBm as well — so far so good. However, plug a second tape recorder input across the mixer output and its 600Ω input impedance interacts with that of the first machine to produce a new combined input impedance of about 300Ω. (Without getting too far into the physics here, this is because the two inputs are wired in parallel.) The result is a reduction in the signal level at each tape recorder input, as the same source signal current now has to be shared between the two destinations, therefore developing half the voltage across each input impedance. A halving of voltage is a 6dB reduction in signal level and, consequently, the tape recorder meters show an input level of about -6dBm instead of 0dBm. This is clearly not a good situation, and is very restrictive in terms of what can be connected to what.

## Voltage Matching & Bridging Inputs

The solution to this problem is to dispense with the idea of matched impedances 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 impedances of around 150Ω or below, with input impedances of at least 10kΩ or above. With the minuscule output impedance and relatively high input impedance, (the cable impedance can be disregarded completely in comparison) the full output voltage should be developed across the input impedance.

Figure 3. In a voltage-matched system, two tape machines can be connected to the same console without an appreciable drop in level at either of the machines — the two parallel 30kOhms impedances are seen as 15kOhms by the source, which is still very high compared to the 150 Ohms output impedance.Relatively high-impedance inputs such as these are called bridging inputs, and 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. (A low impedance is often referred to as 'loading' the output or circuit, because of the high current it demands.)

Let's have another look at our earlier example (see Figure 3), where a console output is feeding two tape machines. Say each machine now has an input impedance of 30kΩ; connecting two in parallel will only reduce the combined input impedance to 15kΩ, which is still substantially higher than the 150Ω output impedance of the console. Hence, the input voltage will be virtually unaffected — I calculate a loss of 0.04dB, in fact! Even connecting a third device to the output, the impedance would only fall to 10kΩ — the level would fall by a further 0.05dB, which I don't think anyone would hear! Because bridging inputs make studio work so much easier, the idea of voltage matching is now employed almost universally in line-level audio equipment, irrespective of the actual reference signal levels used.

 High-impedance Hi-fi Standards Although the vast majority of hi-fi equipment uses the voltage matching concept, there is some which employs a very different strategy, and it is worth knowing about this strange idea lest you ever come across it! The DIN organisation (Deutsches Industrie Normal) defined an interface standard many years ago which uses current sources instead of voltage sources to generate the output signal. The DIN interface usually employs DIN sockets (now better known for their use in MIDI interfaces) — in three-, five-, seven-, or sometimes eight-way configurations. The five-way version is standard for stereo interfaces and can accommodate stereo inputs and outputs simultaneously, with a common earth connection.The significance of using a current source to generate the output is that the signal voltage seen by the receiving device depends almost entirely on its input impedance. The DIN specification states that the current source should give an output voltage of 1mV per 1kΩ of input impedance. Typically, the input impedance of a DIN-compatible unit would be 100kΩ, and so would see an input signal voltage of about 100mV.Hi-fi equipment with phono connectors usually employs the voltage matching concept, with very low output impedance and much higher input impedance (although rarely as high as 100kΩ). Typical signal levels vary between 250mVRMS and 1VRMS, although CD and DVD players are usually specified with an output voltage of 2VRMS.

## Microphones & Preamplifiers

In the early days of microphone development, with ribbon and moving-coil designs being the only high-quality devices available, most microphone and preamplifier systems were designed with impedance-matched interfaces — typically operating at 300Ω, although other standards did exist. Later on, with the introduction of capacitor microphones and their internal impedance converting head amplifiers, the idea of voltage matching was adopted and is retained to this day for all microphone types. There are a few microphone preamplifiers available which are designed specifically for use with vintage ribbon microphones and still include impedance-matched interfaces. However, these are rather specialised devices and are of little practical concern to most of us.

Typically, most microphones therefore have an output impedance of 150-200Ω, and most preamplifier inputs offer an input impedance of between 1.5kΩ and 3kΩ — on the limit of the 'ten times higher' rule of thumb I mentioned earlier. It is a good idea to keep the input impedance of mic amps relatively low (at least compared to typical line inputs) since resistors generate noise when current flows through them; the higher the resistance the greater the noise. Since the signal level from microphones is relatively weak, a lot of gain is generally required, amplifying the resistor noise along the way. This is the reason why mic preamp specs should quote the source impedance when providing the Equivalent Input Noise (EIN) measurement; the lower the source impedance, the lower the noise will be. A good EIN figure can be achieved for the spec sheet by measuring the input stage with a 50Ω source impedance. However, this noise figure will be totally unrealisable with a real-world 200Ω microphone!

## Impedance Considerations With Electric Guitars

The pickups generally used in electric guitars and basses are primarily inductive rather than capacitive (because of the coils used under the strings), and are also highly resistive simply because of the sheer amount of wire involved (typically up to 10kΩ), although different styles and makes of pickup can vary enormously. Since the pick-up presents a relatively high output impedance, it is normal to provide guitar preamp and DI inputs with a hugely high input impedance. A minimum value is typically 470kΩ, but many are over 1MΩ and a few, designed for accepting feeds from magnetic pickups in some acoustic guitars, are rated even higher than this.

If the input has too low an impedance, the most noticeable effect will be a loss of high end — in fact, even using guitar cables with too high a capacitance can audibly reduce high frequencies (see 'Impedance & Frequency Response' box for details of this effect). The sustain is also affected, giving a 'dead' sound.

 Signal Levels: dBm Or dBu? Another inheritance from the telecommunications industry is our 0dB nominal line level. The telecoms industry, because it was interested in the transfer of power, measured audio signals in terms of milliwatts. In fact, the standard signal level was 1mW. The relationship between power (symbol P, measured in Watts), resistance and voltage is:For 1mW into 600Ω, V is therefore 0.775V. Sound familiar? It should, because that is the value we still use today as a standard line-level reference RMS (Root Mean Square) voltage. We measure audio signal amplitudes in terms of decibels for convenience, and the reference value is always 0dB. The nominal telecom signal level was defined as 0dBm — the 'm' signifies a reference of 1mW in 600Ω.When the broadcasting and audio industries moved away from matching impedances and towards bridging inputs, the '1mW in 600Ω' reference became meaningless, but the same nominal signal amplitude was retained. To make this change clear in the specifications the term 0dBu was coined — the 'u' meaning the impedance is unspecified, but assumed high (and therefore not loading the source to any appreciable effect). Thus a 0dBu reference level is still an RMS voltage of 0.775V.

## Loudspeaker Impedance

Most readers will be aware that loudspeakers are quoted with a nominal impedance of usually four, 8, 15 or 16Ω. The last tends to be used with vintage valve amplifiers, the first with automotive and battery-powered systems. Loudspeakers are very complex things, and those with passive crossovers are often challenging for the amplifier(s) to drive. Many loudspeaker manufacturers reproduce plots of the impedance curves of their designs showing impedance against frequency. A cursory examination reveals just how variable the impedance can be, and therefore how difficult it can be for the amplifier to deliver its signal accurately at all frequencies.

In general, amplifiers are designed to have an extremely low output impedance (usually fractions of Ohms) so that the loudspeaker impedance is significantly higher. However, the impedance of the connecting cable can also have an audible effect on the sound quality. For example, the dreaded 'bell flex' so often used with cheap and cheerful systems presents a relatively high resistance and, since it is in series with the loudspeaker, a portion of the amplifier's energy will be dissipated simply in heating the wire. The cable resistance may also interact with the crossover's characteristics.

Figure 4. Here's a way you can connect four 8 Ohm speakers to a single amplifier while maintaining the overall 8 Ohm load.There is a great deal of black magic associated with speaker cables (and line-level interconnects for that matter) by the hi-fi press, most of which, in my opinion at any rate, is complete hogwash. Nothing more than common sense and sensibly engineered equipment is required. By using good-quality, thick cables which are terminated properly, the cable resistance will be sufficiently low to become as irrelevant as the capacitance. While there are plenty of good, high-quality speaker cables available, heavy-duty two-core mains cable is just as good in almost every situation, and considerably cheaper!

Incidentally, it is worth knowing that if you connect loudspeakers in series, the impedance increases by the sum of the individual units. For example, two 8Ω speakers in series present an impedance of 16Ω. Working out the impedance for speakers wired in parallel is slightly more complicated. If the speaker impedances are R1, R2, R3, and so on, the combined impedance is:

For example, two 8Ω speakers in parallel offer an impedance of 4Ω. By combining these two effects you can, for example, connect four 8Ω speakers to an amplifier intended to drive an 8Ω load as in Figure 4 (above). Although each speaker in this configuration will receive less power than a single speaker, the combined power will be almost the same. However, there are advantages to using multiple speakers: each speaker can be cheaper, because it needs to produce less power; and the combined surface area of the speaker cones can be increased, which can be used to improve the system's bass performance — hence the multi-speaker design of some bass guitar cabinets.

 Characteristic Impedance It's not only circuit components that have impedance — cables also have an impedance value, called characteristic impedance. If you thought that a cable was just a couple of pieces of wire with a screening braid wrapped around them, then think again! In fact, every cable exhibits capacitance between the wires and the braid, and inductance along the length of the cable too (although the capacitance typically dominates the impedance value). Consequently, a look through any cable catalogue (Canford Audio's catalogue is particularly useful in this regard) will reveal the characteristic impedances of cables, along with values for their inter-core capacitance per metre of length.One difference between cables and components, however, is that the characteristic impedance of cables doesn't increase appreciably when cables are linked in series (assuming no impedance mismatch at the connection), except where extreme cable lengths are involved. This means that you can freely use passive digital patchbays in matched-impedance digital systems to connect between different pieces of equipment.

Headphones, like loudspeakers, also present a load impedance to the driving amplifier. However, there are three main classes of headphone design — and I'm talking just about impedances here, not the arguments over closed-backed, open-backed, or in-ear designs. The impedance of a headphone is determined by the design of its voice coils — the length and size of wire used, the number of turns around the former, and so on. Consequently, the impedance will affect the volume produced by the headphone — but so too will the strength of the magnet, and several other aspects of the design. The best guide is the quoted sensitivity of the headphone in terms of decibels per milliwatt (dB/mW). The design of the amplifier used to drive the headphones will also have a significant bearing on the output volume.

Broadly, headphones can be categorised into three groups by their impedance: broadcast, professional or portable. The 'broadcast' group have a relatively high impedance, typically of between 1.5kΩ and 2kΩ. The idea behind this relatively high impedance is so that the headphones can be plugged into a patch bay to monitor a signal source without loading it unduly and causing a drop in the level. The ubiquitous Beyer DT100 can be specified with a 2kΩ impedance, for example.

The next group are the 'professional' designs which typically range from 150Ω to 600Ω. Within this group it is often the case that the lower the impedance the higher the volume. It is an obvious marketing ploy, but, given two otherwise similar designs, the one with the lower impedance will sound louder when plugged into the same amplifier — and, of course, some purchasers may be swayed into purchasing one pair of headphones over another simply because of the extra volume. The Sennheiser HD250 is available with a 150Ω impedance, for example.

The third group are the designs intended for use with portable CD players and the like. Power is the product of voltage and current, but, since the supply voltage to the amplifiers is limited (because you're using batteries), more power requires more current. That can only be achieved if the headphones have a low impedance. Typical designs provide impedances in the 8-32Ω region — the Sony MDR7509 is specified with a 24Ω impedance, for example.

Increasingly, people tend to use high-quality 'professional'-impedance headphones with portable equipment, and this is rarely a problem, except that the maximum volume will be reduced compared to a lower-impedance design — which is no bad thing in most cases and could potentially increase the battery life of the player. It is worth noting that most manufacturers offer a variety of impedance options with many of their headphone models — Beyerdynamic are particularly comprehensive in this respect, but it is often worth asking the question if a favoured model appears not to be of a suitable impedance for your application.

## Audio Metering, Video & Digital Audio

To wrap up this discussion of impedance issues, I'm collecting what may seem a strange combination of topics under one heading, but all will make sense shortly. As you will now appreciate, the accurate level metering of audio signals requires a certain knowledge of the interface configuration and the appropriate impedance or voltage matching. In general, outboard meters — whether proper test and measurement devices, or just external meters of some kind — will be designed with high input impedances. This is so that they can be connected across an audio circuit without loading it and affecting the level. After all, it would be pretty silly if plugging the meter in drastically changed the signal level you were trying to measure! With the normal voltage-matched interface arrangements, there is therefore nothing to worry about — you can simply plug the meter across an audio circuit and all will be well.

However, connecting a high-impedance meter straight across the output of a device intended to operate in a matched-impedance environment will produce erroneous results. This is because the source's output is designed to drive into 600Ω — anything else will mess the levels up completely. Test and measurement meters are often equipped with a switchable 600Ω termination facility for exactly this reason.

Although it is extremely rare to find any 600Ω matched-impedance audio equipment outside venerable broadcast institutions like the BBC these days, it is worth considering the issues involved, because they also apply to digital audio and video — both of which are matched-impedance systems. Video interfaces normally operate with 75Ω matched-impedance connections. In other words, outputs source their signals from 75Ω, inputs present 75Ω, and the coaxial cables have a characteristic impedance of 75Ω — nothing else will do!

Figure 5. Although digital word clock inputs and outputs are meant to be impedance matched, it is possible to daisy-chain a number of inputs from a single output if you make sure only to have the 75 Ohms termination impedance at the end of the chain.A lot of video equipment provides switchable 75Ω termination on the input connections, but that is to provide flexibility rather than to denigrate the balanced impedance concept. In a balanced impedance system, provided that the source, destination and cabling all present the required 75Ω impedance characteristic, everything is fine. However, it is often necessary to connect multiple devices to a single output, and that is not strictly allowed in a matched-impedance system. One way around the problem is to connect the inputs of the destination equipment in parallel (by using special T-shaped adaptors to connect from one unit to the next), with only the last providing the necessary 75Ω termination — the others all present a very high input impedance. In this way the source 'thinks' it is only driving one destination, and the correct impedance matching is maintained, provided that the 75Ω termination is at the end of the line of connected equipment.

This same matched impedance concept is used for S/PDIF digital audio signals (on phono or BNC connectors), and also digital audio word clocks. Again, 75Ω interfaces are used with 75Ω coaxial cable. Don't be tempted to use any old bit of screened wire, because the unmatched characteristic impedance will result in reflections and signal attenuation which will either prevent the data transfer completely, or mess it up sufficiently to make the interface extremely unreliable.

Most S/PDIF connections are on a one-to-one basis, so both the source and destination devices present 75Ω impedances, and expect passage over a 75Ω cable. However, word clock signals are frequently distributed to multiple destinations, so many manufacturers have adopted the same kind of approach with their clock inputs as video equipment manufacturers. In other words, the word clock input may be of a high impedance design with a switchable 75Ω termination. The same rules apply here as for video. Only the last piece of equipment in the chain should provide the 75Ω termination — any other arrangement will result in reflections and signal loss. Beware that a lot of digital equipment has only fixed 75Ω impedance on word clock inputs, and in this case it is not possible to daisy-chain a word clock feed. A distribution amplifier will be required instead to provide one-to-one clock feeds, maintaining the impedance matching.

AES-EBU digital audio is also interfaced with an impedance-matched system, this time designed for 110Ω impedances. Again, it is wise to use only cables designed with the appropriate 110Ω characteristic impedance, although I have found that the balanced nature of AES-EBU, combined with the fact that the signal starts off at a very healthy voltage level, makes it far more tolerant of impedance mismatches than either S/PDIF, word clock, or composite video.

The AES-EBU specification states that the interface is intended as a one-to-one system and distribution amplifiers should be used if one output is required to feed several inputs. Having said that, the original AES-EBU specifications allowed for one source to feed directly up to four destinations, and I have often found this works satisfactorily — mainly because of the very robust and tolerant nature of AES-EBU. The potential problem with a passive distribution arrangement like this, though, is that if one receiving device is disconnected, the signal reflections from its unterminated cable will return to the distribution point and interact destructively with the source data, preventing the other destinations from decoding the signals.