Chapter 2

Components

Conductors

It is easy to assume, when wrestling with electronic design, that the active devices will cause most of the trouble. This, like so much in electronics, is subject to Gershwin’s Law: it ain’t necessarily so. Passive components cannot be assumed to be perfect, and while their shortcomings are rarely discussed, they are all too real. In this chapter I have tried to avoid repeating basic stuff that can be found in many places, to allow room for information that goes deeper.

Normal metallic conductors, such as copper wire, show perfect linearity for our purposes, and as far as I am aware, for everybody’s purposes. Ohm’s Law was founded on metallic conductors after all, not resistors, which did not exist as we know them at that time. Georg Simon Ohm published a pamphlet in 1827 entitled ‘The Galvanic Circuit Investigated Mathematically’ while he was a professor of mathematics in Cologne. His work was not warmly received, except by a perceptive few; the Prussian minister of education pronounced that ‘a professor who preached such heresies was unworthy to teach science’. This is the sort of thing that happens when politicians try to involve themselves in science, and in that respect we have progressed little since then.

Although the linearity is generally effectively ideal, metallic conductors will not be perfectly linear in some circumstances. Poorly made connections between oxidized or otherwise contaminated metal parts are capable of generating harmonic distortion at the level of several percent, but this is a property of the contact interface rather than the bulk material, and usually means that the connection is about to fail altogether. A more subtle danger is that of magnetic conductors – the soft iron in relay frames causes easily detectable distortion at power-amplifier current levels.

From time to time some of the dimmer audio commentators speculate that metallic conductors are actually a kind of ‘sea of micro-diodes’, and that non-linearity can be found if the test signal levels are made small enough. This is both categorically untrue and physically impossible. There is no threshold effect for metallic conduction.

I have myself added to the mountain of evidence on this, by measuring distortion at very low signal levels [1].

Copper and Other Conductive Elements

Copper is the preferred metal for conducting electricity in almost all circumstances. It has the lowest resistance of any metal but silver, is reasonably resistant to corrosion, and can be made mechanically strong. Being a heavy metal, it is unfortunately not that common in the earth’s crust, and so is expensive compared with iron and steel. It is, however, cheap compared with silver. The price of both metals varies all the time due to changing economic and political factors, but at the time of writing silver was 100 times more expensive by weight. Given the same cross-section of conductor, the use of silver would only reduce the resistance of a circuit by 5%. Despite this, silver connection wire has been used in some very expensive hi-fi amplifiers; output impedance-matching transformers wound with silver wire are not unknown in valve amplifiers. Since the technical advantages are negligible such equipment is marketed on the basis of indefinable subjective improvements.

Table 2.1 gives the resistivity of the commonly used conductors, plus some insulators to give it perspective. The difference between copper and quartz is of the order of 1025, an enormous range that is not found in many other physical properties.

Table 2.1   Properties of conductors and non-conductors

*A barreter is an incredibly obsolete device consisting of thin iron wire in an evacuated glass envelope. It was typically used for current regulation of the heaters of RF oscillator valves, to improve frequency stability.

Constantan and manganin are resistance alloys with moderate resistivity and a low temperature coefficient. Constantan is preferred as it has a flatter resistance–temperature curve and its corrosion resistance is better.

There are several reasonably conductive metals that are lighter than copper, but their higher resistivity means they require a larger cross-section to carry the same current, so copper is always used when space is limited, as in electric motors, solenoids, etc. However, when size is not the primary constraint, the economics work out differently. The largest use of non-copper conductors is probably in the transmission line cables that are strung between pylons. Here minimal weight is more important than minimal diameter and the cables have a central steel core for strength, surrounded by aluminum conductors.

It is clear that simply spending more money does not automatically bring you a better conductor; gold is a somewhat poorer conductor than copper, and platinum, which is even more expensive, is worse by a factor of 6. Another interesting feature of this table is the relatively high resistance of mercury, nearly 60 times that of copper. This often comes as a surprise; people seem to assume that a metal of such high density must be very conductive, but it is not so. There are many reasons for not using mercury-filled hoses as loudspeaker cables, and their conductive inefficiency is just one. The cost and the insidiously poisonous nature of the metal are two more. Nonetheless, it is reported that the Hitachi Cable company has experimented with speaker cables made from polythene tubes filled with mercury. There appear to have been no plans to put such a product on the market. RoHS compliance might be a problem.

The Metallurgy of Copper

Copper is a good conductor because the outermost electrons of its atoms have a large mean free path between collisions. The electrical resistivity of a metal is inversely related to this electron mean free path, which in the case of copper is approximately 100 atomic spacings.

Copper is normally used as a very dilute alloy known as electrolytic tough pitch (ETP) copper, which consists of very high purity metal alloyed with oxygen in the range of 100–650 ppm. In view of the wide exposure that the concept of oxygen-free copper has had in the audio business, it is worth underlining that the oxygen is deliberately alloyed with the copper to act as a scavenger for dissolved hydrogen and sulfur, which become water and sulfur dioxide. Microscopic bubbles form in the mass of metal but are completely eliminated during hot rolling.

The main use of oxygen-free copper is in conductors exposed to a hydrogen atmosphere at high temperatures. ETP copper is susceptible to hydrogen embrittlement in these circumstances, which arise in the hydrogen-cooled alternators in power stations.

Gold and its Uses

As stated above, gold has a higher resistivity than copper, and there is no incentive to use it as the bulk metal of conductors, not least because of its high cost. However, it is very useful as a thin coating on contacts because it is almost immune to corrosion, though it is chemically attacked by fluorine and chlorine. (If there is a significant amount of either gas in the air then your medical problems will be more pressing than your electrical ones.) Other electrical components are sometimes gold-plated simply because the appearance is attractive. A carat (or karat) is a image part, so 24-carat gold is the pure element, while 18-carat gold contains only 75% of the pure metal. Eighteen-carat gold is the sort usually used for jewellery as it retains the chemical inertness of pure gold but is much harder and more durable; the usual alloying elements are copper and silver.

There are a couple of issues to bear in mind when dealing with gold in electronics; think before you solder gold-plated parts. Gold forms brittle intermetallics with the components of tin–lead solder, giving a weak high-resistance joint that is likely to cause horrible problems in high-current circuits. I have not so far been able to track down any reliable data on interaction between gold and lead-free solder, but I wouldn’t risk it if I were you.

Eighteen-carat gold is widely used in jewellery and does not tarnish, so it is initially puzzling to find that some electronic parts plated with it have a protective transparent coating which the manufacturer claims to be essential to prevent blackening. The answer is that if gold is plated directly on to copper, the copper diffuses through the gold and tarnishes on its surface. The standard way of preventing this is to plate a layer of nickel on to the copper to prevent diffusion, then plate on the gold. I have examined some transparent-coated gold-plated parts and found no nickel layer; presumably the manufacturer finds the transparent coating is cheaper than another plating process to deposit the nickel.

Cable and Wiring Resistance

Electrical cable is very often specified by its cross-sectional area and current-carrying capacity, and the resistance per meter is seldom quoted. This can, however, be a very important parameter for assessing permissible voltage drops and for predicting the crosstalk that will be introduced between two signals when they share a common ground conductor. Given the resistivity of copper from Table 2.1, the resistance R of L meters of cable is simply:

image

Note that the area, which is usually quoted in catalogs in square millimeters, must be expressed here in square meters to match up with the units of resistivity and length. Thus, 5 meters of cable with a cross-sectional area of 1.5 mm2 will have a resistance of:

image

This gives the resistance of our stretch of cable, and it is then simple to treat this as part of a potential divider to calculate the voltage drop down its length.

PCB Track Resistance

It is also useful to be able to calculate the resistance of a printed-circuit board (PCB) track for the same reasons. This is slightly less straightforward to do; given the smorgasbord of units that are in use in PCB technology, determining the cross-sectional area of the track can present some difficulty.

In the USA and the UK, and probably elsewhere, there is inevitably a mix of metric and imperial units on PCBs, as many important components come in dual-in-line packages that are derived from an inch grid; track widths and lengths are therefore very often in thousandths of an inch, universally (in the UK at least) referred to as ‘thou’. Conversely, the PCB dimensions and fixing-hole locations will almost certainly be metric as they interface with a world of metal fabrication and mechanical CAD that (once again, in the UK at least) went metric many years ago. Add to this the UK practice of quoting copper thickness in ounces (the weight of a square foot of copper foil) and all the ingredients for dimensional confusion are in place.

The most common type of PCB laminate is called ‘one-ounce copper’, which means a one-ounce weight of copper foil over a square foot. Less often employed, but still easily obtained, is ‘two-ounce copper’, which naturally has twice the thickness of copper cladding; it is somewhat more expensive. It is most often employed to increase track current-carrying capacity in power amplifiers, switch mode power supplies, and the like. ‘Four-ounce copper’ can be had but it is rarely used and is correspondingly costly.

Given the copper thickness, multiplying by track width and length gives the cross-sectional area. Since resistivity is always in metric units, it is best to convert to metric at this point, so Table 2.2 gives area in square millimeters. This is then multiplied by the resistivity, not forgetting to convert the area to meters for consistency. This gives the ‘resistance’ column in the table, and it is then simple to treat this as part of a potential divider to calculate the usually unwanted voltage across the track.

Table 2.2   Thickness of copper cladding and the calculation of track resistance

For example, if the track in question is the ground return from an 8 Ω speaker load, this is the top half of a potential divider while the track is the bottom half (I am of course ignoring here the fact loudspeakers are not purely resistive loads), and a quick calculation gives the fraction of the input voltage found along the track. This is expressed in the last column of Table 2.2 as attenuation in dB. This shows clearly that loudspeaker outputs should not have common return tracks or the interchannel crosstalk will be dire.

It is very clear from this table that relying on thicker copper on your PCB as a means of reducing path resistance is not very effective. In some situations it may be the only recourse, but in many cases a path of much lower resistance can be made by using 32/02 cable soldered between the two relevant points on the PCB.

PCB tracks have a limited current capability because excessive resistive heating will break down the adhesive holding the copper to the board substrate, and ultimately melt the copper. This is normally only a problem in power amplifiers and power supplies. It is useful to assess if you are likely to have problems before committing to a PCB design, and Table 2.3, based on MIL-standard 275, gives some guidance.

Table 2.3   PCB track current capacity in Amps for a permitted temperature rise

Note that Table 2.3 applies to tracks on the PCB surface only. Internal tracks in a multilayer PCB experience much less cooling, and need to be about three times as thick for the same temperature rise. This factor depends on laminate thickness and so on, and you need to consult your PCB vendor.

Traditionally, overheated tracks could be detected visually because the solder mask on top of them would discolor to brown. I am not sure if this still applies with modern solder mask materials, as in recent years I have been quite successful in avoiding overheated tracking.

PCB Track-to-Track Crosstalk

The previous section described how to evaluate the amount of crosstalk that can arise because of shared track resistances. Another crosstalk mechanism is caused by capacitance between PCB tracks. This is not very susceptible to calculation, so I did the following experiment to put some figures to the problem.

Figure 2.1 shows the set-up; four parallel conductors 1.9 inches long on a standard piece of 0.1-inch pitch prototype board were used as test tracks. These are perhaps rather wider than the average PCB track, but one must start somewhere. The test signal was applied to track A, and track C was connected to a virtual-earth summing amplifier A1.

Figure 2.1: Test circuit for measuring track-to-track crosstalk on a PCB

The tracks B and D were initially left floating. The results are shown as trace 1 in Figure 2.2; the coupling at 10 kHz is −65 dB, which is worryingly high for two tracks 0.2 inch apart. Note that the crosstalk increases steadily at 6 dB per octave, as it results from a very small capacitance driving into what is effectively a short-circuit.

Figure 2.2: Results of PCB track-to-track crosstalk tests

It has often been said that running a grounded screening track between two tracks that are susceptible to crosstalk has a beneficial effect, but how much good does it really do? Grounding track B, to place a screen between A and C, gives trace 2 and has only improved matters by 9 dB – not the dramatic effect that might be expected from screening. The reason, of course, is that electric fields are very much three-dimensional, and if you could see the electrostatic ‘lines of force’ that appear in physics textbooks you would notice they arch up and over any planar screening such as a grounded track. It is easy to forget this when staring at a CAD display. There are of course two-layer and multilayer PCBs, but the visual effect on a screen is still of several slices of 2-D. As Mr Spock remarked in one of the Star Trek films: ‘He’s intelligent, but not experienced. His pattern indicates two-dimensional thinking.’

Grounding track D, beyond receiving track C, gives a further improvement of about 3 dB; this would clearly not happen if PCB crosstalk was simply a line-of-sight phenomenon.

To get more effective screening than this you must go into three dimensions too; with a double-sided PCB you can put one track on each side, with ground plane opposite. With a four-layer board it should be possible to sandwich critical tracks between two layers of ground plane, where they should be safe from pretty much anything. If you can’t do this and things are really tough you may need to resort to a screened cable between two points on the PCB; this is of course expensive in assembly time. If components, such as electrolytics with their large surface area, are talking to each other you may need to use a vertical metal wall, but this costs money. A more cunning plan is to use electrolytics not carrying signal, such as rail decouplers, as screening items.

The internal crosstalk between the two halves of a dual op-amp is very low according to the manufacturer’s specs. Nevertheless, avoid having different channels going through the same op-amp if you can because this will bring the surrounding components into close proximity, and will permit capacitative crosstalk.

Impedances and Crosstalk: A Case History

Capacitative crosstalk between two op-amp outputs can be surprisingly troublesome. The usual isolating resistor on an op-amp output is 47 Ω, and you might think that this impedance is so low that the capacitative crosstalk between two of these outputs would be completely negligible, but you would be wrong.

A stereo power amplifier had balanced input amplifiers with 47 Ω output isolating resistors included to prevent any possibility of instability, although the op-amps were driving only a few centimeters of PCB track rather than screened cables with their significant capacitance. Just downstream of these op-amps was a switch to enable biamping by driving both left and right outputs with the left input. This switch and its associated tracking brought the left and right signals into close proximity, and the capacity between them was not negligible.

Crosstalk at low frequencies (below 1 kHz) was pleasingly low, being better than −129 dB up to 70 Hz, which was the difference between the noise floor and the maximum signal level. (The measured noise floor was unusually low at −114 dBu because each input amplifier was a quadruple noise-canceling type as described in Chapter 14, and that figure includes the noise from an AP System 1.) At higher frequencies things were rather less gratifying, being −96 dB at 10 kHz, as shown by the ‘47R’ trace in Figure 2.3. In many applications this would be more than acceptable, but in this case the highest performance possible was being sought.

Figure 2.3: Crosstalk between op-amp outputs with 47 Ω and 10 Ω output isolating resistors

It was therefore decided to reduce the output isolating resistors to 10 Ω, so the inter-channel capacitance would have less effect. (Checks were done at the time and all through the prototyping and pre-production process to make sure that this would be enough resistance to ensure op-amp stability – it was.) This handily reduced the crosstalk to −109 dB at 10 kHz, an improvement of 13 dB at zero cost. This is the ratio between the two resistor values.

The third trace, marked ‘DIS’, shows the result of removing the isolating resistor from the speaking channel, so no signal reached the biamping switch. As usual, this reveals a further crosstalk mechanism, at about −117 dB, for reducing crosstalk is proverbially like peeling onions. There is layer after layer, and even strong men are reduced to tears.

Resistors

In the past there have been many types of resistor, including some interesting ones consisting of jars of liquid, but only a few kinds are likely to be met with now. These are usually classified by the kind of material used in the resistive element, as this has the most important influence on the fine details of performance. The major materials and types are shown in Table 2.4.

Table 2.4   Characteristics of resistor types

These values are illustrative only, and it would be easy to find exceptions. As always, the official data sheet for the component you have chosen is the essential reference. The sinister significance of the voltage coefficient is explained below.

It should be said that you are most unlikely to come across carbon composition resistors in modern signal circuitry, but they frequently appear in vintage valve equipment so they are included here. They also live on in specialized applications such as switch-mode snubbing circuits, where their ability to absorb a high peak power in a mass of material rather than a thin film is very useful.

Carbon-film resistors are currently still sometimes used in low-end consumer equipment, but elsewhere have been supplanted by the other three types. Note from Table 2.4 that they have a significant voltage coefficient.

Metal-film resistors are now the usual choice when any degree of precision or stability is required. These have no non-linearity problems at normal signal levels. The voltage coefficient is usually negligible.

Metal-oxide resistors are more problematic. Cermet resistors and resistor packages are metal oxide, and are made of the same material as thick-film surface-mount resistors. Thick-film resistors can show significant non-linearity at op-amp-type signal levels, and should be kept out of high-quality signal paths.

Wirewound resistors are indispensable when serious power needs to be handled. The average wirewound resistor can withstand very large amounts of pulse power for short periods, but component manufacturers are often very reluctant to publish specifications on this capability, and endurance tests have to be done at the design stage. The voltage coefficient is usually negligible.

Resistors for general PCB use come in both through-hole and surface-mount types. Through-hole (TH) resistors can be any of the types tabled above; surface-mount (SM) resistors are always either metal film or metal oxide. There are also many specialized types; for example, high-power wirewound resistors are often constructed inside a metal case that can be bolted down to a heat-sink.

Through-Hole Resistors

These are too familiar to require much description. They are available in all the materials mentioned above: carbon film, metal film, metal oxide, and wirewound. There are a few other sorts, such as metal foil, but they are restricted to specialized applications. Conventional through-hole resistors are now almost always 250 mW 1% metal film. Carbon film used to be the standard resistor material, with the expensive metal-film resistors reserved for critical places in circuitry where low temperature coefficient and an absence of excess noise were really important, but as metal film got cheaper so it took over many applications.

TH resistors have the advantage that their power and voltage ratings greatly exceed those of surface-mount versions. They also have a very low voltage coefficient, which for our purposes is of the first importance. On the downside, the spiral construction of the resistance element means they have much greater parasitic inductance.

Surface-Mount Resistors

Surface-mount resistors come in two main formats, the common chip type and the rarer (and much more expensive) MELF format.

Chip surface-mount (SM) resistors come in a flat tombstone format, which varies over a wide size range (see Table 2.5).

Table 2.5   The standard surface-mount resistor sizes with typical ratings

Size L × W

Max. power dissipation

Max. voltage (V)

2512

1 W

200

1812

750 mW

200

1206

250 mW

200

0805

125 mW

150

0603

100 mW

75

0402

100 mW

50

0201

50 mW

25

01005

30 mW

15

MELF surface-mount resistors have a cylindrical body with metal endcaps, the resistive element is metal film, and the linearity is therefore as that of good as that of conventional resistors, with a voltage coefficient of less than 1 ppm. MELF is apparently an acronym for ‘Metal ELectrode Face-bonded’, though most people I know call them ‘Metal Ended Little Fellows’ or something quite close to that.

Surface-mount resistors may have thin-film or thick-film resistive elements. The latter are cheaper and so more often encountered, but the price differential has been falling in recent years. Both thin-film and thick-film SM resistors use laser trimming to make fine adjustments of resistance value during the manufacturing process. There are important differences in their behavior.

Thin-film (metal-film) SM resistors use a nickel–chromium (Ni–Cr) film as the resistance material. A very thin Ni–Cr film of less than 1 μm thickness is deposited on the aluminum oxide substrate by sputtering under vacuum. Ni–Cr is then applied on to the substrate as conducting electrodes. The use of a metal film as the resistance material allows thin-film resistors to provide a very low temperature coefficient, much lower current noise and vanishingly small non-linearity. Thin-film resistors need only low laser power for trimming (one-third of that required for thick-film resistors) and contain no glass-based material. This prevents possible microcracking during laser trimming and maintains the stability of the thin-film resistor types.

Thick-film resistors normally use ruthenium oxide (RuO2) as the resistance material, mixed with glass-based material to form a paste for printing on the substrate. The thickness of the printing material is usually 12 μm. The heat generated during laser trimming can cause microcracks on a thick-film resistor containing glass-based materials, which can adversely affect stability. Palladium/silver (PdAg) is used for the electrodes.

The most important thing about thick-film SM resistors from our point of view is that they do not obey Ohm’s Law very well. This often comes as a shock to people who are used to TH resistors, which have been the highly linear metal film type for many years. They have much higher voltage coefficients than TH resistors, at between 30 and 100 ppm. The non-linearity is symmetrical about zero voltage and so gives rise to third-harmonic distortion. Some SM resistor manufacturers do not specify voltage coefficient, which usually means it can vary disturbingly between different batches and different values of the same component, and this can have dire results on the repeatability of design performance.

Chip-type SM resistors come in standard formats with names based on size, such as 1206, 0805, 0603, and 0402. For example, 0805, which used to be something like the ‘standard’ size, is 0.08 inch by 0.05 inch (see Table 2.5). The smaller 0603 is now more common. Both 0805 and 0603 can be placed manually if you have a steady hand and a good magnifying glass. The 0402 size is so small that the resistors look rather like grains of pepper; manual placing is not really feasible. They are only used in equipment where small size is critical, such as mobile phones. They have very restricted voltage and power ratings, typically 50 V and 100 mW. The voltage rating of TH resistors can usually be ignored, as power dissipation is almost always the limiting factor, but with SM resistors it must be kept firmly in mind.

Recently, even smaller SM resistors have been introduced; for example, several vendors offer 0201, and Panasonic and Yageo offer 01005 resistors. The latter are truly tiny, being about 0.4 mm long; a thousand of them weigh less than a twentieth of a gram. They are intended for mobile phones, palmtops, and hearing aids; a full range of values is available from 10 Ω to 1 MΩ (jumper inclusive). Hand placing is really not an option.

Surface-mount resistors have a limited power-dissipation capability compared with their through-hole cousins, because of their small physical size. SM voltage ratings are also restricted, for the same reason. It is therefore sometimes necessary to use two SM resistors in series or parallel to meet these demands, as this is usually more economic than hand-fitting a through-hole component of adequate rating. If the voltage rating is the issue then the SM resistors will obviously have to be connected in series to gain any benefit.

Resistor Imperfections

It is well known that resistors have inductance and capacitance, and vary somewhat in resistance with temperature. Unfortunately there are other less obvious imperfections, such as excess noise and non-linearity; these can get forgotten because parameters describing how bad they are are often omitted from component manufacturers’ data sheets.

Being components in the real world, resistors are not perfect examples of resistance and nothing else. Their length is not infinitely small and so they have series inductance; this is particularly true for the many kinds that use a spiral resistive element. Likewise, they exhibit stray capacitance between each end, and also between the various parts of the resistive element. Both effects can be significant at high frequencies, but can usually be ignored below 100 kHz unless you are using very high or low resistance values.

It is a sad fact that resistors change their value with temperature. Table 2.4 shows some typical temperature coefficients. This is not likely to be a problem in audio applications, where extreme precision is not required unless you are designing measurement equipment. Carbon-film resistors are markedly inferior to metal film in this area.

Resistor Noise

All resistors, no matter what their resistive material or mode of construction, generate Johnson noise. This is white noise, its level being determined solely by the resistance value, the absolute temperature, and the bandwidth over which the noise is being measured. It is based on fundamental physics and is not subject to negotiation. In some cases it places the limit on how quiet a circuit can be, though the noise from active devices is often more significant. Johnson noise was covered in Chapter 1.

Excess resistor noise refers to the fact that a resistor, with a constant voltage drop across it, generates excess noise in addition to its inherent Johnson noise. According to classical physics, passing a current through a resistor should have no effect on its noise behavior; it should generate the same Johnson noise as a resistor with no steady current flow. In reality, some resistors do generate excess noise when they have a DC voltage across them. It is a very variable quantity, but is essentially proportional to the DC voltage across the component, a typical spec being ‘1 μV/V’, and it has a 1/f frequency distribution. Typically it could be a problem in biasing networks at the input of amplifier stages. It is usually only of interest if you are using carbon- or thick-film resistors – metal-film and wirewound types should have very little excess noise. 1/f noise does not have a Gaussian amplitude distribution, which makes it difficult to assess reliably from a small set of data points. A rough guide to the likely specs is given in Table 2.6.

Table 2.6   Resistor excess noise

Type

Noise (μV/V)

Carbon-film TH

0.2–3

Metal-oxide TH

0.1–1

Thin-film SM

0.05–0.4

Bulk metal-foil TH

0.01

Wirewound TH*

0

*Wirewound resistors are normally considered to be completely free of excess noise.

The level of excess resistor noise changes with resistor type, size, and value in ohms. The relevant factors are discussed below.

Thin-film resistors are markedly quieter than thick-film resistors; this is due to the homogeneous nature of thin-film resistive materials, which are metal alloys such as nickel–chromium deposited on a substrate. The thick-film resistive material is a mixture of fine metal (often ruthenium) oxides and glass particles; the glass is fused into a matrix for the metal particles by high-temperature firing. The higher excess noise levels associated with thick-film resistors are a consequence of their heterogeneous structure, due to the particulate nature of the resistive material. The same applies to carbon-film resistors where the resistive medium is finely divided carbon dispersed in a polymer binder.

A physically large resistor has lower excess noise than a small resistor. In the same resistor range, the highest wattage versions have the lowest noise (see Figure 2.4).

Figure 2.4: The typical variation of excess resistor noise with ohmic value and physical size; this is for a range of carbon-film resistors. The flat part of the plot represents the measurement floor, not a change in noise mechanism

A low ohmic value resistor has lower excess noise than a high ohmic value resistor. Noise in μV per V rises approximately with the square root of resistance (see Figure 2.4 again).

A low value of excess noise is associated with uniform constriction-free current flow; this condition is not well met in composite thick-film materials. However, there are great variations among different thick-film resistors. The most readily apparent relationship is between noise level and the amount of conductive material present. Everything else being equal, compositions with lower resistivity have lower noise levels.

Higher resistance values give higher excess noise since it is a statistical phenomenon related to the total number of charge carriers available within the resistive element; the fewer the total number of carriers present, the greater will be the statistical fluctuation.

Traditionally at this point in the discussion of excess resistor noise, the reader is warned against using carbon composition resistors because of their very bad excess noise characteristics. Carbon composition resistors do still exist – their construction makes them good at handling pulse loads – but are not likely to be encountered in audio circuitry.

One of the great benefits of op-amp circuitry is that it is noticeably free of resistors with large DC voltages across them. The offset voltages and bias currents are far too low to cause trouble with resistor excess noise. However, if you are getting into low-noise hybrid discrete/op-amp stages, such as the moving-coil head amplifier discussed in Chapter 8, you might have to consider it.

To get a feel for the magnitude of excess resistor noise, consider a 100 kΩ, 0.25 W carbon-film resistor with 10 Vacross it. This, from the graph in Figure 2.4, has a current noise parameter of about 0.7 μV/V and so the excess noise will be of the order of 7 μV, which is −101 dBu. This definitely could be a problem in a low-noise preamplifier stage.

Resistor Non-Linearity

Ohm’s Law strictly is a statement about metallic conductors only. It is dangerous to assume that it also invariably applies to ‘resistors’ simply because they have a fixed value of resistance marked on them; in fact resistors – whose main raison d’être is packing a lot of controlled resistance in a small space – do not always adhere to Ohm’s Law very closely. This is a distinct difficulty when trying to make low-distortion circuitry.

Resistor non-linearity is normally quoted by manufacturers as a voltage coefficient, usually the number of parts per million (ppm) that the resistor value changes when one volt is applied. The measurement standard for resistor non-linearity is IEC 6040.

Normal (i.e. lead-through-board) metal-film resistors show perfect linearity at the levels of performance considered here, as do wirewound types. The voltage coefficient is less than 1 ppm. Carbon-film resistors are quoted at less than 100 ppm; 100 ppm is, however, enough to completely dominate the distortion produced by active devices, if it is used in a critical part of the circuitry. Carbon composition resistors, probably of historical interest only, come in at about 350 ppm, a point that might be pondered by connoisseurs of antique equipment. The greatest area of concern over non-linearity is thick-film SM resistors, which have high and rather variable voltage coefficients (more on this below).

Table 2.7 (calculated with SPICE) gives the total harmonic distortion (THD) in the current flowing through the resistor for various voltage coefficients when a pure sine voltage is applied. If the voltage coefficient is significant this can be a serious source of non-linearity.

Table 2.7   Resistor voltage coefficents and the resulting distortion at +15 and +20 dBu

Voltage coefficient (ppm)

THD at +15 dBu (%)

THD at +20 dBu (%)

1

0.00011

0.00019

3

0.00032

0.00056

10

0.0016

0.0019

30

0.0032

0.0056

100

0.011

0.019

320

0.034

0.060

1000

0.11

0.19

3000

0.32

0.58

Distortion here is assumed to be second order, and so varies proportionally with level. Third-order distortion, which will be dominant if a resistor has no steady voltage across it, rises as the square of level.

My own test set-up is shown in Figure 2.5. The resistors are usually of equal value, to give 6 dB attenuation. A very-low-distortion oscillator that can give a large output voltage is necessary; the results in Figure 2.6 were taken at a 10 Vrms (+22 dBu) input level. Here thick-film SM and TH resistors are compared. The ‘gen-mon’ trace at the bottom is the record of the analyzer reading the oscillator output and is the measurement floor of the AP System 1 used. The TH plot is higher than this floor, but this is not due to distortion. It simply reflects the extra Johnson noise generated by two 10 kΩ resistors. Their parallel combination is 5 kΩ, and so this noise is at −115.2 dBu. The SM plot, however, is higher again, and the difference is the distortion generated by the thick-film component.

Figure 2.5: Test circuit for measuring resistor non-linearity. The not-under-test resistor R2 in the potential divider must be a metal-film type with negligible voltage coefficient

Figure 2.6: Surface-mount resistor distortion at 10 Vrms input, using 10 kΩ 0805 thick-film resistors

For both thin-film and thick-film SM resistors non-linearity increases with resistor value, and also increases as the physical size (and hence power rating) of the resistor shrinks. The thin-film versions are much more linear (see Figures 2.7 and 2.8).

Figure 2.7: Non-linearity of thin-film surface-mount resistors of different sizes. THD is in dB rather than percent

Figure 2.8: Non-linearity of thick-film surface-mount resistors of different sizes

Sometimes it is appropriate to reduce the non-linearity by using multiple resistors in series. If one resistor is replaced by two with the same voltage coefficient in series, the THD in the current flowing is halved. Similarly, three resistors reduce THD to a third of the original value. There are obvious economic limits to this sort of thing, but it can be useful in specific cases, especially where the voltage rating of the resistor is a limitation.

Capacitors

Capacitors are diverse components. In the audio business their capacitance ranges from 10 pF to 100,000 μF, a ratio of 1010. In this they handily outdo resistors, which usually vary from 0.1 Ω to 10 MΩ, a ratio of only 108. However, if you include the 10 GΩ bias resistors used in capacitor microphone head amplifiers, this range increases to 1011. There is, however, a big gap between the 10 MΩ resistors, which are used in DC servos, and 10 GΩ microphone resistors; I am not aware of any audio applications for 1 GΩ resistors.

Capacitors also come in a wide variety of types of dielectric, the great divide being between electrolytic and non-electrolytic types. Electrolytics used to have much wider tolerances than most components, but things have recently improved and ±20% is now common. This is still wider than for typical non-electrolytics, which are usually ±10% or better.

This is not the place to reiterate the basic information about capacitor properties, which can be found from many sources. I will simply note that real capacitors fall short of the ideal circuit element in several ways, notably leakage, equivalent series resistance (ESR), dielectric absorption, and non-linearity.

Capacitor leakage is equivalent to a high value resistance across the capacitor terminals, and allows a trickle of current to flow when a DC voltage is applied. It is usually negligible for nonelectrolytics, but is much greater for electrolytics.

ESR is a measure of how much the component deviates from a mathematically pure capacitance. The series resistance is partly due to the physical resistance of leads and foils, and partly due to losses in the dielectric. It can also be expressed as tan δ (tan-delta). Tan-delta is the tangent of the phase angle between the voltage across and the current flowing through the capacitor.

Dielectric absorption is a well-known phenomenon; take a large electrolytic, charge it up, and then make sure it is full discharged. You can use a screwdriver across the terminals if you’re not too worried about either the screwdriver or the capacitor. Wait a few minutes, and the charge will partially reappear, as if from nowhere. This ‘memory effect’ also occurs in nonelectrolytics to a lesser degree; it is a property of the dielectric, and is minimized by using polystyrene, polypropylene, NPO ceramic, or polytetrafluoroethylene dielectrics. Dielectric absorption is invariably simulated by a linear model composed of extra resistors and capacitances, and does not in itself appear to be a source of non-linearity.

Capacitor non-linearity is undoubtedly the least known of these shortcomings. A typical RC low-pass filter can be made with a series resistor and a shunt capacitor, and if you examine the output with a distortion analyzer, you will find to your consternation that the circuit is not linear. If the capacitor is a non-electrolytic type with a dielectric such as polyester, then the distortion is relatively pure third harmonic, showing that the effect is symmetrical. For a 10 Vrms input, the THD level may be 0.001% or more. This may not sound like much but it is substantially greater than the mid-band distortion of a good op-amp. Capacitor non-linearity is dealt with at greater length below.

Capacitors are used in audio circuitry for three main functions, where their possible nonlinearity has varying consequences:

  1. Coupling or DC-blocking capacitors. These are usually electrolytics, and if properly sized have a negligible signal voltage across them at the lowest frequencies of interest. The properties of the capacitor are pretty much unimportant unless current levels are high; power amplifier output capacitors can generate considerable mid-band distortion [2]. Much nonsense has been talked about mysterious coupling capacitor properties, but it is all nonsense. For small-signal use, as long as the signal voltage across the capacitor is kept low, non-linearity is not normally detectable. The capacitance value is non-critical, as it has to be, given the wide tolerances of electrolytics.

  2. Supply filtering or decoupling capacitors. These are electrolytics if you are filtering out supply-rail ripple, etc., and non-electrolytics, usually around 100 nF, when the task is to keep the supply impedance low at high frequencies and so keep op-amps stable. The capacitance value is again non-critical.

  3. Setting time-constants, for example the capacitors in the feedback network of an RIAA amplifier. This is a much more demanding application than the other two. Firstly, the actual value is now crucially important as it defines the accuracy of the frequency response. Secondly, there is by definition significant signal voltage across the capacitor and so nonlinearity can be a serious problem. Non-electrolytics are normally used; sometimes an electrolytic is used to define the lower end of the bandwidth, but this is a bad practice likely to introduce distortion at the bottom of the frequency range. Small-value ceramic capacitors are used for compensation purposes.

In Subjectivist circles it is frequently asserted that it is essential for good sound quality to bypass all coupling electrolytics with small non-electrolytic capacitors. This is quite untrue, as a moment’s thought shows. If there is no signal voltage across the main coupling capacitor, what effect could adding a much smaller capacitor in parallel have?

Capacitor Non-Linearity Examined

When attempting the design of linear circuitry, everyone knows that inductors and transformers with ferromagnetic core material can be a source of non-linearity. It is, however, less obvious that capacitors and even resistors can show non-linearity and generate some unexpected and very unwelcome distortion. Resistor non-linearity has been dealt with earlier in this chapter; let us examine the shortcomings of capacitors.

The definitive work on capacitor distortion is a magnificent series of articles by Cyril Bateman in Electronics World [3]. The authority of this work is underpinned by Cyril’s background in capacitor manufacture. (The series is long because it includes the development of a low-distortion THD test set in the first two parts.)

Capacitors generate distortion when they are actually implementing a time-constant – in other words, when there is a signal voltage across them. The normal coupling or DC-blocking capacitors have no significant signal voltage across them, as they are intended to pass all the information through, not to filter it or define the system bandwidth. Capacitors with no signal across them do not generally produce distortion at small-signal current levels. This was confirmed for all the capacitors tested below. However, electrolytic types may do so at power amplifier levels where the current through them is considerable, such as in the output coupling capacitor of a power amplifier [2].

Non-Electrolytic Capacitor Non-Linearity

It has often been assumed that non-electrolytic capacitors, which generally approach an ideal component more closely than electrolytics, and have dielectrics constructed in a totally different way, are free from distortion. It is not so. Some non-electrolytics show distortion at levels that are easily measured, and can exceed the distortion from the op-amps in the circuit. Non-electrolytic capacitor distortion is primarily third harmonic, because the non-polarized dielectric technology is basically symmetrical. The problem is serious, because non-electrolytic capacitors are commonly used to define time-constants and frequency responses (in RIAA equalization networks, for example) rather than simply for DC blocking.

Very small capacitances present no great problem. Simply make sure you are using the C0G (NP0) type, and so long as you choose a reputable supplier, there will be no distortion. I say ‘reputable supplier’ because I did once encounter some allegedly C0G capacitors from China that showed significant non-linearity [4].

Middle-range capacitors, from 1 nF to 1 μF, present more of a problem. Capacitors with a variety of dielectrics are available, including polyester, polystyrene, polypropylene, poly-carbonate, and polyphenylene sulfide, of which the first three are the most common. (Note that what is commonly called ‘polyester’ is actually polyethylene terephthalate.)

Figure 2.9 shows a simple low-pass filter circuit which, in conjunction with a good THD analyzer, can be used to get some insight into the distortion problem; it is intended to be representative of a real bit of audio circuitry. The values shown give a pole frequency, or −3 dB roll-off point, at 710 Hz. Since it might be expected that different dielectrics give different results (and they definitely do) we will start off with polyester, the smallest, most economical, and therefore the most common type for capacitors of this size.

Figure 2.9: Simple low-pass test circuit for non-electrolytic capacitor distortion

The THD results for a microbox 220 nF, 100 V capacitor with a polyester dielectric are shown in Figure 2.10, for input voltages of 10, 15, and 20 Vrms. They are unsettling.

Figure 2.10: Third-harmonic distortion from a 220 nF, 100 V polyester capacitor, at 10, 15, and 20 Vrms input level, showing peaking around 400 Hz

The distortion is all third harmonic and peaks at around 300–400 Hz, well below the pole frequency, and even with input limited to 10 Vrms will exceed the non-linearity introduced by op-amps such as the 5532 and the LM4562. Interestingly, the peak frequency changes with applied level. Below the peak, the voltage across the capacitor is constant but distortion falls as frequency is reduced, because the increasing impedance of the capacitor means it has less effect on a circuit node at 1 kΩ impedance. Above the peak, distortion falls with increasing frequency because the low-pass circuit action causes the voltage across the capacitor to fall.

The level of distortionvaries with different samples of the same type of capacitor; six of the above type were measured and the THD at 10 Vrms and 400 Hz varied from 0.00128% to 0.00206%. This puts paid to any plans for reducing the distortion by some sort of cancellation method.

The distortion can be seen in Figure 2.10 to be a strong function of level, roughly tripling as the input level doubles. Third-harmonic distortion normally quadruples for doubled level, so there may well be an unanswered question here. It is, however, clear that reducing the voltage across the capacitor reduces the distortion. This suggests that if cost is not the primary consideration, it might be useful to put two capacitors in series to halve the voltage, and the capacitance, and then double up this series combination to restore the original capacitance, giving the series-parallel arrangement in Figure 2.11. The results are shown in Table 2.8, and once more it can be seen that halving the level has reduced distortion by a factor of 3 rather than 4.

Figure 2.11: Reducing capacitor distortion by series-parallel connection

Table 2.8   The reduction of polyester capacitor distortion by series-parallel connection

Input level (Vrms)

Single capacitor

Series-parallel capacitors

10

0.0016%

0.00048%

15

0.0023%

0.00098%

20

0.0034%

0.0013%

The series-parallel arrangement obviously has limitations in terms of cost and PCB area occupied, but might be useful in some cases.

Clearly polyester gives significant distortion, despite its extensive use in audio circuitry of all kinds. The next dielectric we will try is polystyrene. Capacitors with a polystyrene dielectric are extremely useful for some filtering and RIAA-equalization applications because they can be obtained at a 1% tolerance at up to 10 nF at a reasonable price. They can be obtained in larger sizes at an unreasonable, or at any rate much higher, price.

The distortion test results are shown in Figure 2.12 for a 4n7 2.5% capacitor; the series resistor R1 has been increased to 4.7 kΩ to keep the −3 dB point inside the audio band, and it is now at 7200 Hz. Note that the THD scale has been extended down to a subterranean 0.0001%, and if it was plotted on the same scale as in Figure 2.10 it would be bumping along the bottom of the graph. Figure 2.12 in fact shows no distortion at all, just the measurement noise floor, and the apparent rise at the high-frequency (HF) end is simply due to the fact that the output level is decreasing, because of the low-pass action, and so the noise floor is relatively increasing. This is at an input level of 10 Vrms, which is about as high as might be expected to occur in normal op-amp circuitry. The test was repeated at 20 Vrms, which might be encountered in discrete circuitry, and the results were the same – no measurable distortion.

Figure 2.12: The THD plot with three samples of 4n7, 2.5% polystyrene capacitors, at 10 Vrms input level. The reading is entirely noise

The tests were done with four samples of 10 nF 1% polystyrene from LCR at 10 and 20 Vrms, with the same results for each sample. This shows that polystyrene capacitors can be used with confidence; this finding is in complete agreement with Cyril Bateman’s findings [5].

Having settled the issue of capacitor distortion below 10 nF, we need now to tackle its capacitor values greater than 10 nF. Polyester having proven unsatisfactory, the next most common dielectric is polypropylene, and I might as well say at once that it was with considerable relief that I found these were effectively distortion-free in values up to 220 nF. Figure 2.13 shows the results for four samples of a 220 nF 250 V 5% polypropylene capacitor from RIFA. Once more the plot shows no distortion at all, just the noise floor, the apparent rise at the HF end being increasing relative noise due to the low-pass roll-off. This is also in agreement with Cyril Bateman’s findings [6]. Rerunning the tests at 20 Vrms gave the same result – no distortion. This is very pleasing, but there is a downside. Polypropylene capacitors of this value and voltage rating are much larger than the commonly used 63 or 100 V polyester capacitor, and more expensive.

Figure 2.13: The THD plot with four samples of 220 nF, 250 V, 5% polypropylene capacitors, at 10 Vrms input level. The reading is again entirely noise

It was therefore important to find out if the good distortion performance was a result of the 250 V rating, and so I tested a series of polypropylene capacitors with lower voltage ratings from different manufacturers. Axial 47 nF 160 V 5% polypropylene capacitors from Vishay proved to be THD-free at both 10 and 20 Vrms. Likewise, microbox polypropylene capacitors from 10 to 47 nF, with ratings of 63 and 160 V from Vishay and Wima, proved to generate no measurable distortion, so the voltage rating appears not to be an issue. This finding is particularly important because the Vishay range has a 1% tolerance, making them very suitable for precision filters and equalization networks. The 1% tolerance is naturally reflected in the price.

The only remaining issue with polypropylene capacitors is that the higher values (above 100 nF) appear to be currently only available with 250 or 400 V ratings, and that means a physically big component. For example, the EPCOS 330 nF 400 V 5% part has a footprint of 26 mm by 6.5 mm, with a height of 15 mm. One way of dealing with this is to use a smaller capacitor in a capacitance multiplication configuration, so a 100 nF, 1% component could be made to emulate 470 nF. It has to be said that the circuitry for this is only straightforward if one end of the capacitor is connected to ground.

When I first started looking at capacitor distortion, I thought that the distortion would probably be lowest for the capacitors with the highest voltage rating. I therefore tested some RF-suppression X2 capacitors, rated at 275 Vrms, which translates into a peak or DC rating of 389 V. These are designed to be connected across the mains and therefore have a thick and tough dielectric layer. For some reason manufacturers seem to be very coy about saying exactly what the dielectric material is, normally describing them simply as ‘film capacitors’. A problem that surfaced immediately is that the tolerance is 10% or 20%, not exactly ideal for precision filtering or equalization. A more serious problem, however, is that they are far from distortion-free. Four samples of a 470 nF X2 capacitor showed THD between 0.002% and 0.003% at 10 Vrms. Clearly a high voltage rating alone does not mean low distortion.

Electrolytic Capacitor Non-Linearity

Cyril Bateman’s series in Electronics World [3] included two articles on electrolytic capacitor distortion. It proved to be a complex subject, and many long-held assumptions (such as ‘DC biasing always reduces distortion’) were shown to be quite wrong. Distortion was in general a good deal higher than for non-electrolytic capacitors.

My view is that electrolytics should never, ever, under any circumstances, be used to set time-constants in audio. There should be a time-constant early in the signal path, based on a non-electrolytic capacitor, that determines the lower limit of the bandwidth, and all the electrolytic-based time-constants should be much longer so that the electrolytic capacitors can never have significant signal voltages across them and so never generate measurable distortion. There is of course also the point that electrolytics have large tolerances, and cannot be used to set accurate time-constants anyway.

However, even if you obey this rule, you can still get into deep trouble. Figure 2.14 shows a simple high-pass test circuit designed to represent an electrolytic capacitor in use for coupling or DC blocking. The load of 1 kΩ is the sort of value that can easily be encountered if you are using low-impedance design principles. The calculated −3 dB roll-off point is 3.38 Hz, so the attenuation at 10 Hz, at the very bottom of the audio band, will be only 0.47 dB; at 20 Hz it will be only 0.12 dB, which is surely a negligible loss. As far as frequency response goes, we are doing fine. But examine Figure 2.15, which shows the measured distortion of this arrangement. Even if we limit ourselves to a 10 Vrms level, the distortion at 50 Hz is 0.001%, already above that of a good op-amp. At 20 Hz it has risen to 0.01%, and by 10 Hz a most unwelcome 0.05%. The THD is increasing by a ratio of 4.8 times for each octave fall in frequency – in other words, increasing faster than a square law. The distortion residual is visually a mixture of second and third harmonic, and the levels proved surprisingly consistent for a large number of 47 μF 25 V capacitors of different ages and from different manufacturers.

Figure 2.14: High-pass test circuit for examining electrolytic capacitor distortion

Figure 2.15: Electrolytic capacitor distortion from the circuit in . Input level 10, 15, and 20 Vrms

Figure 2.15 also shows that the distortion rises rapidly with level; at 50 Hz going from an input of 10 to 15 Vrms almost doubles the THD reading. To underline the point, consider Figure 2.16, which shows the measured frequency response of the circuit with 47 μF and 1 kΩ; note the effect of the capacitor tolerance on the real versus calculated figures. The roll-off that does the damage, by allowing an AC voltage to exist across the capacitor, is very modest indeed, less than 0.2 dB at 20 Hz.

Figure 2.16: The measured roll-off of the high-pass test circuit for examining electrolytic capacitor distortion

Having demonstrated how insidious this problem is, how do we fix it? As we have seen, changing capacitor manufacturer is no help. Using 47 μF capacitors of higher voltage does not work – tests showed there is very little difference in the amount of distortion generated. An exception was the sub-miniature style of electrolytic, which was markedly worse.

The answer is simple – just make the capacitor bigger in value. This reduces the voltage across it in the audio band, and since we have shown that the distortion is a strong function of the voltage across the capacitor, the amount produced drops more than proportionally. The result is seen in Figure 2.17, for increasing capacitor values with a 10 Vrms input.

Figure 2.17: Reducing electrolytic capacitor distortion by increasing the capacitor value. Input 10 Vrms

Replacing C1 with a 100 μF 25 V capacitor drops the distortion at 20 Hz from 0.0080% to 0.0017%, an improvement of 4.7 times; the voltage across the capacitor at 20 Hz has been reduced from 1.66 Vrms to 790 mVrms. A 220 μF 25 V capacitor reduces the voltage across itself to 360 mV, and gives another very welcome reduction to 0.0005% at 20 Hz, but it is necessary to go to 1000 μF 25 V to obtain the bottom trace, which is indistinguishable from the noise floor of the AP-2702 test system. The voltage across the capacitor at 20 Hz is now only 80 mV. From this data, it appears that the AC voltage across an electrolytic capacitor should be limited to below 80 mVrms if you want to avoid distortion. I would emphasize that these are ordinary 85ºC rated electrolytic capacitors, and in no sense special or premium types.

This technique can be seen to be highly effective, but it naturally calls for larger and somewhat more expensive capacitors, and larger footprints on a PCB. This can be to some extent countered by using capacitors of lower voltage, which helps to bring back down the CV product and hence the capacitor volume. I tested 1000 μF 16 V and 1000 μF 6V3 capacitors, and both types gave exactly the same results as the 1000 μF 25 V part in Figure 2.17, with useful reductions in CV product and can size. This does of course assume that the capacitor is, as is usual, being used to block small voltages from op-amp offsets to prevent switch clicks and pot noises rather than for stopping a substantial DC voltage.

The use of large coupling capacitors in this way does require a little care, because we are introducing a long time-constant into the circuit. Most op-amp circuitry is pretty much free of big DC voltages, but if there are any, the settling time after switch-on may become undesirably long.

More information on capacitor distortion in specific applications can be found in chapters 3 and 5.

Inductors

For several reasons, inductors are unpopular with circuit designers. They are relatively expensive, often because they need to be custom made. Unless they are air-cored (which limits their inductance to low values) the core material is a likely source of non-linearity. Some types produce substantial external magnetic fields, which can cause crosstalk if they are placed close together, and similarly they can be subject to the induction of interference from other external fields. In general they deviate from being an ideal circuit element much more than resistors or capacitors.

It is rarely, if ever, essential to use inductors in signal-processing circuitry. Historically they were used in tone controls, before the Baxandall configuration swept all before it, and their last applications were probably in mid EQ controls for mixing consoles and in LCR filters for graphic equalizers. These too were gone by the end of the 1970s, being replaced by active filters and gyrators, to the considerable relief of all concerned (except inductor manufacturers).

The only place where inductors are essential is when the need for galvanic isolation, or enhanced EMC immunity, makes input and output transformers desirable, and even then they need careful handling (see Chapters 14 and 15 on line-in and line-out circuitry).

References

[1]  D. Self, Ultra-low-noise amplifiers and granularity distortion, JAES (November 1987), pp. 907–915.

[2]  D. Self, Audio Power Amplifier Handbook, fifth ed, Focal Press, 2009, p. 43 (amp output cap).

[3]  C. Bateman, Capacitor sound? Parts 1–6, Electronics World (July 2002 to March 2003).

[4]  D. Self, Audio Power Amplifier Design Handbook, fifth ed., Focal Press, 2009, p. 205 (C0G cap).

[5]  C. Bateman, Capacitor sound? Part 3, Electronics World (October 2002), p. 16, 18.

[6]  C. Bateman, Capacitor sound? Part 4, Electronics World (November 2002) p. 47.

Small Signal Audio Design; ISBN: 9780240521770

Copyright © 2010 Elsevier Ltd; All rights of reproduction, in any form, reserved.

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