818 Series
Phase and Phases
Match Considerations
1 kHz to 1.28 MHz
Phase Deviation from Theoretical:
EXAMPLE: Phase Match Calculation
The phase response of the amplifiers and the
capacitance of the frequency control switches of the 818
series contribute to the overall phase response and
cause it to deviate from theoretical. For the higher
frequency models ( -4 and -5 ), where the cutoff
frequencies can be programmed up to 1.28MHz, the
deviation from theoretical can be substantial.
∆Φ(f)max = 0.02° x Φτ(f) + 4.0° x f/fc x fmax/1.28MHz
4.0° - L8L
3.0° - L8B & L8D80
2.0° - L8L
∆Φ(f)typ =0.5 x ∆Φ(f)max
where: ∆Φ(f) = phase match at frequency f
Φτ (f) = theoretical phase shift at f
Figure 1 is a normalized plot of the phase deviation from
theoretical for an 818L8E-5 for programmed cutoff
frequencies from 5kHz ( fc min ) to 1.28MHz (fc max ).
For fc of 5kHz, the deviation from the 323° theoretical
phase shift is 2° but for fc of 1.28MHz the deviation is
78°. This set of curves can be used to estimate the
deviation from theoretical phase for other models in the
818 series.
f
= frequency of interest
f max = maximum fc of the model
fc
= frequency to which the filter is
programmed
Eg. - for an 818L8E-3, the phase deviation from
theoretical at a frequency of 192kHz, when the cutoff
frequency fc is programmed to 384kHz is:
Figure 1 represents a "maximum deviation from
theoretical phase" situation. Other models (i.e. -1 to -4)
will exhibit a similar set of phase deviation curves with
the phase scale being reduced by the ratio of the f max
of the model to the f max of the -5. For example, an L8E-
1, whose programming frequency range is from 1kHz to
256kHz (1/5 of the range of the -5 model) will have a
similar set of phase deviation curves but the maximum
phase deviation, at the highest frequency setting (fc
max), will be approximately 1/5 that of the -5 model (78/5
= 15.6°). The other programmed settings of the -1 will
also produce proportionally reduced phase deviations.
f/fc = 192kHz/384kHz = 0.5, fmax = 768kHz
Φτ(f) = 133° (from data table at f/fc = 0.5)
Phase Match:
∆Φ(f)max = 0.02° x Φτ(f) + 4.0° x f/fc x fmax/1.28MHz
= 0.02 x (-133°) + 4.0° x 0.5 x 768kHz/1.28MHz
= 2.66° + 1.20° = +3.86°
∆Φ(f)typ =0.5 x ∆Φ(f)max = 0.5° x 3.86° = 1.93°
818L8E Phase Deviation (in degrees “°”) from
2
Theoretical vs. Normalized Input Frequency
programmed setting of fc
Unit to Unit Phase Match
f/fc 5kHz 10kHz 20kHz 40kHz 80kHz 160kHz 320kHz 640kHz 1.28MHz
0.10 0.15 0.18 0.17 0.08 -0.12 -0.52 -1.18 -2.57 -5.32
0.20 0.30 0.32 0.30 0.17 -0.39 -1.03 -2.41 -5.17 -10.76
0.30 0.34 0.42 0.40 -0.18 -0.57 -1.59 -3.66 -7.89 -16.29
0.40 0.20 0.40 0.50 -0.20 -0.90 -2.30 -5.10 -10.80 -22.10
0.50 0.20 0.32 0.60 -0.40 -1.20 -3.00 -6.70 -14.00 -28.20
0.60 0.00 0.00 -0.10 -0.80 -1.90 -4.10 -8.70 -17.70 -35.10
0.70 -0.21 -0.30 -0.60 -1.30 -2.70 -5.40 -11.00 -21.80 -42.60
0.80 -0.50 -0.60 -1.30 -2.10 -3.80 -7.20 -13.90 -26.90 -51.30
0.85 -0.80 -1.00 -1.80 -2.80 -4.70 -8.40 -15.80 -30.10 -56.40
0.90 -1.20 -1.60 -2.50 -3.70 -5.80 -10.00 -18.40 -33.80 -62.30
0.95 -1.90 -2.40 -3.50 -4.80 -7.30 -12.00 -21.10 -38.30 -69.20
1.00 -2.50 -3.30 -4.60 -6.20 -8.90 -14.10 -24.30 -43.30 -77.50
The actual phase shift through a filter at a frequency " f "
is determined by its programmed frequency " fc ", the
theoretical phase response of the transfer function (B, L,
E, or D80) and the phase deviation from theoretical
which in turn depends upon component tolerances, the
model # (i.e. -1 through -5) and frequency to which it is
programmed. It is therefore not possible to have a
meaningful unit to unit phase match that is specified by a
single number.
For a group of the same model type and number,
programmed to the same frequency, the unit to unit
phase match can be approximated as a percentage of
the theoretical phase shift with a correction term added
to accommodate amplifier induced phase deviations.
5
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