Nominal & Load Impedance

October 26, 2013 in AV Design Tips, The Basics by Sam Davisson

Why we love speakers

AKA Impedance Part II

Ok, before I jump into this I’ll apologize to anyone who is offended by the cartoon. It’s a bit of an inside joke with a good friend of mine and I couldn’t resist the urge

Nominal impedance in electrical and audio engineering refers to the approximate designed impedance of an electrical circuit or device.

Actual impedance varies with frequency changes. It is possible for that variance to be quite large. Despite that, it is normal to speak of nominal impedance as if it were a constant resistance with no reactive components. Which is often far from the truth. Nominal impedance is referring to a specific point on the frequency response of the circuit being considered.

Loudspeaker impedance’s are kept relatively low so that the required audio power can be transmitted without the use of high voltages. The most common nominal impedance for loudspeakers is 8 Ω. Also used are 4 Ω and 16 Ω.

The once common 16 Ω is now mostly reserved for high frequency compression drivers since the high frequency end of the audio spectrum does not usually require much power to reproduce the sound.

Diagram showing the variation in impedance of a typical mid-range loudspeaker. Nominal impedance is determined at the lowest point after resonance.

Diagram showing the variation in impedance of a typical mid-range loudspeaker. Nominal impedance is determined at the lowest point after resonance.

The impedance of a loudspeaker is not constant across all frequencies. In a typical loudspeaker the impedance will rise with increasing frequency from its dc value (see diagram) until it reaches a point of mechanical resonance. Following resonance, the impedance falls to a minimum and then begins to rise again. Speakers are usually designed to operate at frequencies above their resonance, and for this reason it is the usual practice to define nominal impedance at this minimum.

The ratio of the peak resonant frequency to the nominal impedance can be as much as 4:1. It is, however, possible for the low frequency impedance to actually be lower than the nominal impedance. A given audio amplifier may not be capable of driving this low frequency impedance even though it is capable of driving the nominal impedance, a problem that can be solved with the use of crossover filters.

Note that is also may be possible to solve the problem above by underrating the amplifier. This is not a solution I would recommend but it is a possibility

Speaker Basics

Getting very basic here, our use of the word SPEAKER is the shortened form of the word LOUDSPEAKER and it refers to a device that converts electrical signals into sound waves that we can hear. A loudspeaker has several parts:

  • Cabinet – It should be noted that the cabinet performs a much greater function than to simply house the components that make up the loudspeaker. The discussion of which is well beyond the scope of this post. But if you truly want to understand loudspeakers and how they function to produce audiophile quality sound it is a subject worth delving into.
  • Driver (aka speaker) – Converts electrical energy into sound waves (more on this to come)
  • Crossover Network – As we will discuss, speakers are designed to reproduce specific ranges of frequencies. The crossover network filters the frequencies sending only the frequencies that can be used to a specific driver. Passive crossovers will typically be installed inside of the cabinet. Speakers meant for high end audio use will either have switches allowing for the passive network to be bypassed or have the passive crossover removed altogether. In these instances an external crossover, typically built within the systems digital signal processor (DSP), will be used.

Speakers (drivers) are constructed much in the same manner as a musical instrument in the fine tolerances and attention to detail make all the difference to the sound quality. Large speakers are suited for low frequencies, small speakers – high frequencies. Each speaker can only function efficiently and with linearity within 3 octaves of it’s design. Theoretically a single speaker would have to change diameter from 1" – 24′ to maintain a similar level and dispersion over the complete frequency spectrum.

Speaker cross section

The majority of drivers consist of paper or plastic molded into a cone shape, loosely suspended in a frame so as to easily move back and forth to vibrate the air. Glued to the back of the cone is a coil of wire aka voice coil suspended within a strong magnetic field. Passing electricity through the wire causes a magnetic field around the wire which attracts or repels which in turn causes the cone to move back and forth. The larger the magnet and voice coil the greater the power and efficiency of the driver. Because of the tight tolerances no two speakers are truly identical.

Load Impedance

For the load impedance discussion I’ll use the Ω symbol for resistance. Z is the symbol for impedance. As we have discussed impedance could be stated as resistance that varies with frequency.

Load impedance is the load speakers represent to the amplifier. The maximum power rating of an amp is always in reference to the load impedance. For example if the amplifier is rated for 100W (watts) of power into a 4Ω load it is only capable of producing 100 watts with a 4Ω load. If you connect an 8Ω load, the amplifier will only be capable of producing 50W of power. The higher the load impedance the cooler and more reliable the amplifier will be, and the lower the internal distortion. But it will produce less power.

Conversely, if you present a 2Ω load the amplifier will attempt to deliver 200W of power which could quite possibly damage the amplifier. If you don’t see smoke and flames the amplifier will run much hotter and less reliably.

Calculating Speaker Impedance with Multiple Speakers

Parallel, Series and Series Parallel Speakers

Calculating speaker impedance follows the same laws of electronics as for purely resistive circuits. For speakers in parallel divide the speakers nominal impedance by the number of speakers. Therefore, 2 8Ω speakers have a nominal impedance of 4Ω and 4 8Ω speakers have a nominal impedance of 2Ω.

For speakers connected in series, add the nominal impedance’s of the speakers. Therefore 2 8Ω speakers nominal impedance is 16Ω.

You should only connect speakers in a series-parallel configuration with an even number of speakers. First calculate the nominal impedance for the series speakers. Then calculate the 2 series pairs in parallel. In other words, 2 8Ω speakers in series is 16Ω. The 2 sets of series speakers in parallel would then represent a nominal impedance of 8Ω

Connecting speakers in series and series parallel may be essential in certain applications where many speakers are required to be connected to one amplifier. However connecting speakers in series causes the distortion of each speaker to be reflected into the others. But connecting speakers in series does not effect the reliability of the speakers or amplifier.

Amplifier Classes

October 20, 2013 in AV Design Tips, The Basics by Sam Davisson

6v6_top_sideAmplifier Classes

When I first started this article I fully intended to finish up Impedance by discussing amplifiers, speakers and the effects of impedance on audio quality. That plan changed. I think amplifier classes deserve to be a post of their own and need to be discussed before any meaningful continuation of the impedance discussion. Besides, thinking about all this along with trying to research to find out exactly what a Class G and Class H amplifier was has given me a splitting headache. 😉

This picture looks eerily like one of my early Heath Kit assemblies and if I remember correctly it taught me the value of keeping a fire extinguisher nearby when working with electronic components you were not familiar with. For those who may not know about Heath Kit, they were the originator of DIY electronic projects. You could by a box of parts and instructions from them to build just about any electronic device of the time.

Amplifier Classes

There are complete books on amplifiers and the differing classes of amplifiers. Im not going into that depth here this is the basics after all. Also, don’t expect a discussion of every class of amplifier in existence. Classes C, E and F are more typically found in RF applications than audio applications.

Class A
In a Class A amplifier, the output devices are continuously conducting for the entire cycle, or in other words there is always bias current flowing in the output devices. This topology has the least distortion and is the most linear, but at the same time is the least efficient at about 20%

Class B
This type of amplifier operates in the opposite way to Class A amplifiers. The output devices only conduct for half the sinusoidal cycle (one conducts in the positive region, and one conducts in the negative region), or in other words, if there is no input signal then there is no current flow in the output devices. This class of amplifier is obviously more efficient than Class A, at about 50%, but has some issue with linearity at the crossover point, due to the time it takes to turn one device off and turn the other device on. In other words, it is not distortion free.

Class AB
This type of amplifier is a combination of the above two types, and is the most common type of power amplifier in use. Here both devices are allowed to conduct at the same time, but just a small amount near the crossover point. Hence each device is conducting for more than half a cycle
but less than the whole cycle, so the inherent non-linearity of Class B designs is overcome, without the inefficiencies of a Class A design. Efficiencies for Class AB amplifiers is about 50%. This amplifier remains the amplifier of choice for the true audiophile.

The above amplifiers are known as linear amplifiers.

Class D
This class of amplifier is a switching or PWM amplifier. In this type of amplifier, the switches are either fully on or fully off, significantly reducing the power losses in the output devices. Efficiencies of 90-95% are possible. The audio signal is used to modulate a PWM carrier signal which drives the output devices, with the last stage being a low pass filter to remove the high frequency PWM carrier frequency.

The primary differences between linear (Class A and Class AB) amplifiers and switching (Class D) digital amplifiers is the efficiency. This is the whole reason for the invention of Class D amplifiers. Linear amplifiers are inherently very linear in terms of performance (therefore very distortion free), but are also very inefficient when it comes to power, whereas a Class D amplifier is much more efficient from a power standpoint but suffer from added noise and distortions due to the switching nature and additional filters.

Classes G & H
Honestly, before I started writing this I had heard of these classes and understood they were "improvements" to the Class AB amp in that they are supposed to provide distortion free audio with much greater power efficiencies. In doing the research for this article I found that I probably had about as clear of an understanding as anyone else.

The general consensus seems to be that Class-G runs from a low voltage rail until the signal goes beyond a certain voltage, and then a higher rail (or rails) is switched in. Class-H refines this to use a variable higher voltage rail (or rails), also known as a modulated rail or use a ‘bootstrap’ capacitor that lifts the rails as needed, but cannot maintain them at the full voltage for more than a few cycles.

Multiple rail amplifiers usually allow significantly higher efficiency than single-rail Class-AB design. The more rail levels are used, the higher the efficiency, assuming they’re spaced properly. While in all reality it is impossible, efficiencies can reach 100 percent with an infinite number of voltage rails.

Multiple rail amplifiers typically use only two voltage rails, which amounts to more than 80 percent theoretical efficiency at maximum power. Using more rails becomes impractical due to added power supply complexity, but with four rail voltages, efficiency at maximum power can reach 90 percent theoretically.

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