ANSI/SCTE 16 2001R2007

Appendix 1 – Hum Modulation Derivation
The equation for a TV sinewave amplitude modulated carrier is:
y(t) = B[1 − (k / 2)(1 + cosω m t)]cosω
c
t
(A -1)
where B is the peak amplitude of the RF carrier and k is the modulation factor which is equal to:
M pk−pk
k = , k ≤ 1
B
and k is related to the conventional AM modulation index by the equation:
(A - 2)
k =
2m
( 1+
m)
where m is the conventional AM modulation index.
If the peak-to-peak amplitude variation in time is kB, and this amplitude variation is considered
to be hum modulation, hum is defined as.
AM Mod(dB) = 20Log =
B
( kB ) 20Log( k) (A
Hum modulation is simply a measurement of k, which is the ratio of the peak-to-peak hum on the
carrier to the peak of the RF carrier (B).
- 3)
k =
Hum
B
pk−pk
(A - 4)
Figure 2 shows a graphical representation of hum modulation using a continuous wave (CW)
carrier as an example.
Hum pk-pk
V peak (Peak Voltage of RF Carrier)
Carrier Voltage
Time
Figure 2
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