Thermal noise is generated by any device operating above a temperature of absolute zero. The amount of thermal noise generated is a function of bandwidth and temperature. For a television system with a 75-ohm impedance and operating at 68 degrees Fahrenheit, a channel with a 4-MHz bandwidth has a noise floor (the minimum noise level possible) of -59 dBmV. A 300-kHz-wide channel on the same system has a noise floor of -70 dBm V. The following equation gives the noise floor of a system with a bandwidth B.
En = -125
+
1OIog(B) dBmVAppendix E has details on the source of these figures and of other calculations used in this section.
Noise Figure
The noise figure of an amplifier is the amount of noise that it contributes to signals that it amplifies. It is a property of the amplifier and cannot be changed by alignment.
Increasing the signal level at the amplifier's input changes the carrier-to-noise (C/N) ratio, but does not change the amplifier's noise contribution. An amplifier with a noise figure of 7 dB raises the noise floor of the 4-MHz system from -59 to -52 dBm V. In a cascaded system, the noise contributed by the amplifiers increases by 3 dB every time the number of amplifiers is doubled. The following table lists noise figure for several values of cascaded amplifiers.
Table 5-1.
Effect of Cascading Amplifiers on Noise Figure
Amplifiers in Cascade System Noise Figure (dB)
1 Catalog spec. of amplifier
2 Catalog spec.
+
3 dB4 Catalog spec.
+
6 dB8 Catalog spec.
+
9 dB16 Catalog spec.
+
12 dB32 Catalog spec.
+
15 dBThis relationship can also be expressed in the following equation:
F = Fa
+
IOlog(N) dBwhere F = noise figure of the system including all amplifiers Fa = noise figure of one amplifier
N = number of amplifiers in cascade
Also, the noise floor of a cascaded 4-MHz system can be computed with
En = -59
+
Fa+
IOlog(N) dBmVSystem Carrier-to-Noise Ratio
Carrier-to-Noise (C/N) ratio is the difference between the input signal level and the noise floor. For an input signal of 10 dBm V, the C/N ratio of the single-amplifier example system (with amplifier noise figure of 7 dB) is 62 dB.
To calculate the C/N of a cascaded trunk system, use the following rule: the C/N ratio decreases by 3 dB every time the number of amplifiers is doubled. This can be stated mathematically in the following formula (derived in appendix E).
C/N = C/NO - IOlog(N)
where C/N = the C/N ratio of the system including all cascaded amplifiers C/NO = the C/N ratio of one amplifier
= -Noise Floor
+
Input Level- Noise Figure N = the number of amplifiersFor a system with 32 amplifiers in cascade, a 59 dBm V noise floor, a 10 dBm V input level (typical), and a 7 dB noise figure, its C/N can be calculated as follows.
C/N = 62 - 1010g(32)
= 62 -15
= 47 dB
For convenience, the CATV /broadband industry has related the following C/N values to subjective evaluations of picture quality (table 5-2). A system's C/N ratio should be greater than or equal to 43 dB. The worst case value is measured at the farthest point of each branch.
Table 5-2.
Picture Quality for C/N Values
C/N (dB) Picture Quality Rating
45 Excellent, no distortion
35 Fine, distortion just perceptible
29 Passable, distortion perceptible
25 Marginal
Noise at a Splitter/Combiner
The effects of noise in a bidirectional network are not identical for both directions. One factor contributing to the difference is the passive signal splitter. This component divides one signal travelling in the forward direction into two or more signals for distribution along different paths. In the return direction, this device works as a combiner. It combines signals from two or more paths into a single signal for transmission to the headend. The following discussion describes what happens at a splitter.
~ Forward Direction
Figure 5-6 (a) shows two carrier signals at the common port of a splitter, and the resulting signal and noise levels that appear at each leg. The same output spectrum appears at both output legs. The carrier Signals at frequencies Fl and F2 are decreased in amplitude by 3 dB. The noise level is also reduced by 3 dB.
~ Return Direction
Figure 5-6 (b) shows two different carrier signals, one at each of the two input legs of the combiner. Each carrier signal is attenuated by about 3 dB after passing through the device on its way to the headend.
Noise, however, is a different matter. To calculate the worst-case condition, assume that noise at input port A is in phase with noise at input port B. The noise from each leg is attenuated by 3 dB after passing to output port C. Since the components making up the noise in both paths are in phase, they add together at port C. The result is an output noise level that is the same as the input noise level.
The result is a decrease in C/N ratio of 3 dB.
For combiners with more than 2 input legs, the attenuation is greater, and there could be a decrease in the noise level at the output leg. However, the decrease in signal level is still greater than that of the noise, so the C/N ratio could be degraded.
For this reason, noise effects in the return path must be considered separately in the design of a cable system. Be sure that the C/N ratio at the headend from the farthest transmitter is adequate for good receptIon.
FORWARD SPECTRUM
v
N
TO HEADEND 4 - - -
---fC ... ) ___ ~: ..
V/2@ ®
N/2~i£lU,Q.w.w.w.LC..l1fJd
F1 F2
V/2 N
RETURN SPECTRUM
(a) Splitter
TO HEADEND ... -
@
----l() :
~~-~---®
(b) Combiner Figure 5-6. Noise at a Splitter/Combiner
v
N
v
N