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Chapter 12
Reference Information

12.1 ISO Frequency Centres

This list, shown in Table 12.1 is a standard list of frequencies that can be used for various things such as the centre frequencies for graphic equalizers. The numbers are used a multipliers for the decades within the audio range. For example, if you were building an equalizer with two-third-octave frequency centres, the filters would have centre frequencies of 25 Hz, 40 Hz, 63 Hz, 100 Hz, 160 Hz, 250 Hz, 400 Hz, 630 Hz, 1000 Hz, 1600 Hz, 2500 Hz, 4000 Hz, 6300 Hz, 10000 Hz, and 16000 Hz.








112 Oct16 Oct13 Oct12 Oct23 Oct1 Oct






1 1 1 1 1 1
1.06
1.12 1.12
1.18
1.25 1.25 1.25
1.32
1.4 1.4 1.4
1.5
1.6 1.6 1.6 1.6
1.7
1.8 1.8
1.9
2 2 2 2 2
2.12
2.24 2.24
2.36
2.5 2.5 2.5 2.5
2.65
2.8 2.8 2.8
3
3.15 3.15 3.15
3.35
3.55 3.55
3.75
4 4 4 4 4 4
4.25
4.5 4.5
4.75
5 5 5
5.3
5.6 5.6 5.6
6
6.3 6.3 6.3 6.3
6.7
7.1 7.1
7.5
8 8 8 8 8
8.5
9 9
9.5







Table 12.1: ISO Frequency Centres

Use the numbers listed in the table as multipliers. For example, if you were building a one-octave equalizer, then its frequency centres would use the right-most column of numbers. In Hz, these would be 10 Hz, 20 Hz, 40 Hz, 80 Hz, 100 Hz, 200 Hz, 400 Hz, 800 Hz, 1 kHz, 2 kHz, 4 kHz, 8 kHz, 10 kHz, 20 kHz and so on. If you’re really paying attention here, you’ll notice that these aren’t really octave divisions... because 1 kHz is not one octave above 800 Hz.

12.2 Resistor Colour Codes

If you go to the resistor store, you can buy different types of resistors in different sizes. Some fancy types will have the resistance stamped right on them, but most just have bands of different colours around them as is shown in Figure 12.1.


PIC

Figure 12.1: A typical moulded composition resistor.

The bands are used to indicate a couple of pieces of information about the resistor. In particular, you can find out both the resistance of the device, as well as its tolerance.

Firstly, let’s talk about what the tolerance of a resistor is. Unfortunately, it’s practically impossible to make a resistor that has exactly the resistance that you’re looking for in your circuit. Instead of guaranteeing a particular value such as 1 kΩ, the manufacturer tells you that the resistance is approximately 1 kΩ, some percentage. For example, you’ll see something like 1 kΩ, 20%. Therefore, if you measure the resistor, you’ll see that it has a value between 800 Ω and 1.2 kΩ. If you want better precision than that, you’ll have to do one of two things. You’ll either have to spend more money to get resistors with a tighter tolerance, or you’ll have to hand-pick them yourself by measuring one by one.

So, how do we tell what the specifications of a resistor are just by looking at it? Take a look at Figure 12.2. You’ll see that each band has a label attached to it. Reading from left to right (the right side of the resistor doesn’t have a colour band) we have the 1st and 2nd digits, the multiplier and the tolerance. Using Table 12.2 we can figure out what the shown resistor is.


PIC

Figure 12.2: A typical moulded composition resistor showing the meanings of the coloured bands.







Colour DigitMultiplierCarbon Film-type
Tolerance Tolerance





Black 0 1 20% 0
Brown 1 10 1% 1%
Red 2 100 2% 2%
Orange 3 1,000 3%
Yellow 4 10,000 GMV
Green 5 100,000 5% (alt) 0.5%
Blue 6 1,000,000 6% 0.25%
Violet 7 10,000,00012.5% 0.1%
Gray 8 0.01 (alt) 30% 0.05%
White 9 0.1 (alt) 10% (alt)
Silver 0.01 (pref) 10% (pref)10%
Gold 0.1 (pref) 5% (pref) 5%
No colour 20%






Table 12.2: The corresponding meanings of the colour bands on a resistor [Mandl, 1973]. (GMV stands for Guaranteed minimum value

The colour bands on the resistor in Figure 12.2 are red, green, violet and silver. Table 12.3 shows how this combination is translated into a value.






1st digit2nd digitMultiplierTolerance




red green violet silver
2 5 10,000,00010%





Table 12.3: Using Table 12.2, the colour bands can be used to find that the resistor in Figure 12.1 has a value of 250,000,000 Ω or 250 MΩ, 10%.

12.3 Greek Alphabet





Letter small Capital



Alpha α A
Beta β B
Gamma γ Γ
Delta δ Δ
Epsilon ϵ E
Zeta ζ Z
Eta η H
Theta θ Θ
Iota ι I
Kappa κ K
Lambda λ Λ
Mu μ M
Nu ν N
Xi ξ Ξ
Omicron o O
Pi π Π
Rho ρ P
Sigma σ Σ
Tau τ T
Upsilon υ Υ
Phi ϕ or φ Φ
Chi χ X
Psi ψ Ψ
Omega ω Ω




Table 12.4: Greek letters

12.3.1 Commonly used letters

There are a number of letters that have common usage that make them sort of unavailable for other uses. I’ve put the really typically used ones below in alphabetical order.

Δ – the difference between two things

λ - wavelength

μ – micro, or * 10-6

π – the constant Pi, or, truncated to 50 places after the decimal,
3.141 592 653 589 793 238 462 643 383 279 502 884 197 169 399 375 10

Σ – the addition of

τ – time constant. See Section [].

ω – radian frequency. 2πcf

Ω – Ohms, a unit of impedance, either electrical, acoustical or mechanical.