1 kHz to 1.28 MHz

818 Series

Phase and Phases

Match Considerations

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Phase Deviation from Theoretical:

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.

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.

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.

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.

EXAMPLE: Phase Match Calculation

∆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

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:

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

Theoretical vs. Normalized Input Frequency

programmed setting of fc

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

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