Magnus Encyclopedia

The P page

Phase is is an concept directly connected to repetetiv waveform. The phase is an relative measurement to tell where in the cycle an event is. Phase is measured as an angle due to its strong relationship with sine and cosine functions. Diffrences in phase will cause great changes when two otherwise normal signals is added and therefore is phase and phase difference of great importance.

Phase Accumulator
An device which is infact is an integrator used for the purpose of an oscillator. The output level of the integrator is said to be the phase position of the oscillator. The input level will be an value setting the phasor speed and this will be linear to frequency. The phase position is reseted after the integrator has reached the maximum phase. In an digital implementation is the phase relative so that the overflow is ignored and in this sense it will automatically reset. In an analog implementation must the capacitor in the integrator be emptied using an short cursuit transistor which is activated at the maximum level. Many analog VCOs build upon the phase accumulator principle even thougth it is selldom used as a term for them. The waveform from an phase accumulator is an sawtooth waveform.

Phase Comparator
An device which compares the phase of two applied signals. There exists several diffrent types of comparators which all have their characteristics. The phase comparator and its characteristics are important in phased locked loop cursuits.

Phase Locked Loop
Phase Locked Loop is a technique in which an phase comparator will compare the phase of an input signal and the VCO in the loop. The output of the phase comparator is being filtered and the resulting voltage will control the VCOs frequency. This way will the loop stabilize in such a state that the phase of the input signal and the VCO is equal. The type of phase comparator will create diffrent cases of phase lock. The filter will greatly effect the swing in, stability and tracking properties of the loop. It is common to let an frequency divider cursuit be inserted in the loop between the VCO and the phase comparator so that the frequency of the VCO is divided by a fixed number before being compared with the input signal. This will force the loop to stabilise at the multiple frequency of the input signal, an property of great usefullness. An PLL can also be used to reduce the time jitter of a signal if the VCO is more stable than the input signal is.

Phase Modulation
Phase modulation is a modulation method in which the phase of the signal is altered instead of the frequency or amplitude. Pure phase modulation is selldom seen in synthesizers.

An device in which a signal is phase shifted using an allpass filter and then is the original signal and the phase shifted signal summed together in order to create one or more phase out's (or zeroes as they are called in the LaPlace/s-plane). The number of zeros created depends on the degree of the allpass filter. The allpass filters frequency is then changed by a control voltage which typhically is generated from an LFO so that the zeroes is swept in the frequency range. Typhically will an phasor contain controls over LFO speed, modulation depth (how much the LFO signal may change the frequency of the allpass filter), effect depth (the output mixing, the amount of allpass signal being mixed in) and usually is there an color control which regulates the feedback.

An theoretical complex waveform generator which follows
          (o + jw)t      ot   jwt      ot
a(t) = A e          = A e   e     = A e  (cos wt + j sin wt)

A = Initial amplitude
o = Exponential amplitude time factor (1/s)
w = Angular frequency (rad/s)
t = time
a(t) = Output amplitude as function of time

See Phase Locked Loop.

See Phase Modulation.


  1. A prefix is a modifier of the meaning of some word or expression which is put before that word or expression.
  2. A notation form for mathematical formulas for which the operand is put before the operators. Also known as Polish notation.
  3. A scale modifier which rescales the scale of some unit. The SI standard has assigned letters and names to a series of power of 10 prefixes (known as the SI prefixes). These are:

    SI Prefixes
    LetterNameFactor (exp)Factor (nr)
    YYotta10^24 1 000 000 000 000 000 000 000 000
    ZZetta10^21 1 000 000 000 000 000 000 000
    EExa10^18 1 000 000 000 000 000 000
    PPeta10^15 1 000 000 000 000 000
    TTera10^12 1 000 000 000 000
    GGiga10^9 1 000 000 000
    MMega10^6 1 000 000
    kkilo10^3 1 000
    hhecto10^2 100
    dadeka10^1 10
    ddeci10^-1 0.1
    ccenti10^-2 0.01
    mmili10^-3 0.001
    umicro10^-6 0.000 001
    nnano10^-9 0.000 000 001
    mpico10^-12 0.000 000 000 001
    ffemto10^-15 0.000 000 000 000 001
    aatto10^-18 0.000 000 000 000 000 001
    zzepto10^-21 0.000 000 000 000 000 000 001
    yyocto10^-24 0.000 000 000 000 000 000 000 001

    A prefix does not mean anything all by itself, it is just a modifier to a number measured in some unit. Both the number and unit must be explicitly present in order to form a meaning. However, a prefix may not need to be present to form a meaningfull number. The prefix is a shorthand notation with strict rules associated with it.

    One may never combine two prefixes to form the meaning of another prefix. Example:

                  -6    -6           -12
    1 uuF = 1 * 10  * 10   F = 1 * 10    F = 1 pF
                  3     -12           -9
    1 kpF = 1 * 10  * 10    F = 1 * 10   F = 1 nF
    In the above examples where two common incorect uses of prefixes converted into their proper forms. It is essential that correct forms are being used to avoid confusion, and this comes from real-life experiances!

    As important as using correct forms is the selection of the correct prefix and scaling of the number. For all prefixes (except hecto, deka, deci and centi) shall the prefix be selected so that the number follows the range criteria 1000 > n' >= 1. The n' is the rescaled version of the number n which is to be represented. The numbers relate by this formula:

    n = n' * pf
    n = number to be represented
    n' = mantissa part of the number, as being written with the prefix
    pf = the prefix factor.
    4711 A = 4.711 kA
    0.79 A = 790 mA

    There are a number of prefixes which exist in natural languages which seems to create somewhat of a confusion. It is worth noting that there is a difference between Brittish English and American English. They are:

    Natural Language Prefixes
    World nameU.S.A. nameFactor (exp)Factor (nr)
    millionmillion10^6 1 000 000
    milliardbillion10^9 1 000 000 000
    billiontrillion10^12 1 000 000 000 000
    billiardquadrillion10^15 1 000 000 000 000 000
    trillionquantillion10^18 1 000 000 000 000 000 000


Pulse Width Modulation
Pulse Width modulation is the principle for getting a pulse shaped waveform for which the pulse width relative to the period of the waveform may be modulated. An PWM can be done with a simple comparator cursuit if being feed with either triangle or sawtooth waveform.

See Pulse Width Modulation.

(C) 1997, 1998, 1999
Magnus Danielson <cfmd at bredband dot net>