Participación de la metiltransferasa de histonas SDG8 en la regulación de la dormición de semillas

In Example 5.1 the effect of the various system elements on the received power was calculated. It is also necessary, however, to calculate the impact of noise on the system, since it is eventually the ratio of signal power to noise power (SNR) which will determine the system performance.

The major noise contributions will usually come from the receiver itself, although external noise contributions may also be significant in systems such as fixed satellite links (Chapter 7).

In any case, the total noise associated with the system can be calculated by assuming that the system consists of a two-port network, with a single input and a single output as shown in Figure 5.2. The network is characterised by a gain G, being the ratio of the signal power at the output to the signal power at its input, and by a noise factor F. The noise factor is the ratio between the output noise power of the element divided by G (i.e. referred to the input) and the input noise.

The noise power available at the input of the network from a resistor with an absolute temperature of T K is [Connor, 82]

PN ¼ kTB ð5:11Þ

where k is Boltzmann’s constant¼ 1:379  10^23W Hz^1K^1, T is the absolute temperature of the input noise source [K], B is the effective noise bandwidth of the system [Hz]¹. It is assumed that the network is impedance matched to the resistance. The noise factor is then

F¼N_out Nin

¼N_out

kTB ð5:12Þ

N o is e f a c to r, G T

F

Figure 5.2: A noisy two-port network representing a complete system

1This is the bandwidth of an ideal rectangular filter which would produce the same power as the real filter.

Basic Propagation Models 93

where Noutis the output noise power of the element referred to the input, i.e. the actual noise output power divided by G.

F depends on the design and physical construction of the network. Its value in decibels is the noise figure of the network,

FdB¼ 10 log F ð5:13Þ

The numerical value of the noise power [dBW] can be expressed approximately as Noutj_dBW¼ FdB 204 þ 10 log B ð5:14Þ where T¼ 290 K (23 C) is assumed. Equivalently, using [dBm]

Noutj_dBm¼ FdB 174 þ 10 log B ð5:15Þ An alternative approach is to characterise the network by an equivalent input noise temperature Te. This is the temperature of a noise source which, when placed at the input of the network, yields the same output noise as if the network were noiseless, i.e.

N_out¼ kTB þ kTeB¼ kðT þ TeÞB ð5:16Þ Hence

F¼N_out Nin

¼kðT þ TeÞB

kTB ¼ 1 þT_e

T ð5:17Þ

Usually, B will simply be the intermediate frequency (IF) bandwidth of the receiver.

Example 5.2

A receiver in a digital mobile communication system has a noise bandwidth of 200 kHz and requires that its input SNR should be at least 10 dB when the input signal is

104 dBm. (a) What is the maximum permitted value of the receiver noise figure? (b) What is the equivalent input noise temperature of such a receiver?

Solution

(a) The overall SNR, expressed in [dB], is

SNR¼ Ps N

where P_s is the input signal power [dBW] and N is the noise power of the receiver referred to its input [dBW].

From Eq. (5.12),

N¼ 10 logðFkTBÞ so

SNR¼ Ps N ¼ Ps FdB 10 logðkTBÞ

94 Antennas and Propagation for Wireless Communication Systems

Rearranging,

FdB¼ Ps SNR  10 logðkTBÞ

¼ ð104  30Þ  10  10 logð1:38  10^23 290  200  10³Þ

¼ 7:0 dB

(b) From Eq. (5.17)

T_e¼ TðF  1Þ ¼ 290ð10^7:0=10 1Þ ¼ 1163 K using 290 K as a reference value.

A complete system can be characterised by a cascade of two-port elements, where the ith element has gain G_i and noise factor F_i (Figure 5.3). Each element could consist of an individual module within a receiver, such as an amplifier or filter, or one of the elements within the channel such as the antenna, feeder or some source of external noise.

The gain G of the complete network is then simply given by

G¼ G1 G2     GN ð5:18Þ

while the overall noise factor is given by

F¼ F1þF₂ 1 G1

þF₃ 1 G1G2

þ    þ F_N 1

G1G2     GN1 ð5:19Þ Equivalently, the overall effective noise temperature of the network, Te, can be written in terms of the effective noise temperatures of the individual elements as

Te¼ Te1þTe2

G1

þ Te3

G1G2

þ    þ TeN

G1G2     GN1 ð5:20Þ It is important to note from Eqs. (5.19) and (5.20) that the noise from the first element adds directly to the noise of the complete network, while subsequent contributions are divided by the gains of the earlier elements. It is therefore important that the first element in the series has a low noise factor and a high gain, since this will dominate the noise in the whole system. As a result, receiver systems often have a separate low noise amplifier (LNA) placed close to the antenna, often at the top of the mast and sometimes directly attached to the feed of a dish antenna in order to overcome the impact of the feeder loss.

G₁ F₁

G₂

F₂

...

N

Figure 5.3: A cascade of two-port elements

Basic Propagation Models 95

An important special case of a two-port element is an attenuator, which has passive components only and a gain G¼ 1=L, where L is the attenuator insertion loss. This might be a feeder cable linking an antenna and a receiver. In this case, assuming the attenuator is itself at reference temperature T, Eq. (5.12) shows

F¼Nout

More detail is available in [Connor, 82].

Example 5.3

A receiver is made up of three main elements: a preamplifier, a mixer and an IF amplifier with noise figures 3 dB, 6 dB and 10 dB, respectively. If the overall gain of the receiver is 30 dB and the IF amplifier gain is 10 dB, determine the minimum gain of the preamplifier to achieve an overall noise figure of no more than 5 dB. If its gain is set to this minimum, what would the system noise figure become if the noise figure of the IF amplifier is increased to 20 dB?

Solution

The receiver is modelled as a three-element network, with individual noise factors F₁¼ 2, F2¼ 4 and F3¼ 10, where subscripts 1, 2 and 3 represent the preamplifier, mixer and IF amplifier, respectively. Since the overall gain is 30 dB, we have G1G2G3¼ 1000 and G3¼ 10, so G1G2¼ 100.

From Eq. (5.19), the overall noise factor is F¼ F1þF2 1

This is clearly a very small increase on the previous figure, since the result is highly insensitive to the noise figure of the final element in the cascade.

96 Antennas and Propagation for Wireless Communication Systems