G= Gain kT. RI 凡L T=290K RaT。+T6 W-4kRBn+下 FIGURE 73.8 Equivalent input noise and noise factor. F=(Py(B)/R2)(G2Pw(B)/R1)=(Py(B)/(4kTRBG2) (73.30) Fis seen to be independent of R,, but not R. To compare two noise factors, the same source must be used In the ideal noiseless case, F=l, but as the noise level in the device increases, Fincreases. Because this is a power ratio, we may take the logarithm, called the noise ratio, which NE=10 logo(F=10 logo(Pyx( B))-10 logo(4kTRBG2 (73.31) a The noise power output Pr(B)of an actual device is a superposition of the amplified source thermal noise Pww(B)and the device noise, i. e, Pry (B)=G2Pww(B)+(device noise). The output noise across R, can be measured by putting a single frequency(in the passband) source generator S(n)as input. First, S(n) is turned off, and the output rms voltage Y(o) is measured and the output power Prw (B)is recorded. This is the sum of the thermal available power and the device noise. Next, S(n)is turned on and adjusted until the output power doubles, i.e., until the output power Pr(w(B)+ Pxs)(B)=2Px w(B). This Pss(B) is recorded. Solving for Pns(B)=Prw(B), we substitute this in F= Pr(w(B)/(G Pww(B))to obtain F=Pns (B)/(G2. PwuB))=(GPss(B))/(G4kTRB)=Pss( B)/4kTRB (73.32) a better way is to input white noise w(t) in place of S(t)(a noise diode may be used). The disadvantages of noise factors are(1)when the device has low noise relative to thermal noise the noise factor has value close to 1;(2)a low resistance causes high values; and (3)increasing the source resistance decreases the noise factor while increasing the total noise in the circuit [Ott, 1988, p. 216]. Thus, accuracy is not good. For cascaded devices, the noise factors can be conveniently computed[see Buckingham, 1985, P. 67; or Ott, 1988, p. 228] Equivalent Input Noise shot noise(see below) and other noise can be modeled by equivalent thermal noise that would be generated in an input resistor by increased temperature. Recall that the(maximum)incremental available power(output) in a frequency bandwidth dfis Pwr(f= kTdffrom Eq (73. 27). Figure 73. 8(b) presents the situation. Let the resistor be the noise source at temperature T. with thermal noise W(n). Then ELW(n2]=4kT Rdf, by Eq (73.24 yquist's result). Let the open circuit output noise power at Ri be ely(r2. The incremental available noise power Prr(df) at the output(Ri= R)can be considered to be due to the resistor R having a higher temperature and an ideal (noiseless)device, usually an amplifier. We must find a temperature T at which a pseudothermal e 2000 by CRC Press LLC© 2000 by CRC Press LLC F = (PYY(B)/RL)/(G 2PWW(B)/RL) = (PYY(B))/(4kTRBG 2) (73.30) F is seen to be independent of RL , but not R. To compare two noise factors, the same source must be used. In the ideal noiseless case, F = 1, but as the noise level in the device increases, F increases. Because this is a power ratio, we may take the logarithm, called the noise ratio, which is NF = 10 log10(F) = 10 log10(PYY(B)) – 10 log10(4kTRBG2) (73.31) The noise power output PYY (B) of an actual device is a superposition of the amplified source thermal noise G2 PWW (B) and the device noise, i.e., PYY (B) = G2PWW (B) + (device noise). The output noise across RL can be measured by putting a single frequency (in the passband) source generator S(t) as input. First, S(t) is turned off, and the output rms voltage Y(t) is measured and the output power PY(W)(B) is recorded. This is the sum of the thermal available power and the device noise. Next, S(t) is turned on and adjusted until the output power doubles, i.e., until the output power PY(W)(B) + PY(S)(B) = 2PY(W)(B). This PSS (B) is recorded. Solving for PY(S)(B) = PY(W)(B), we substitute this in F = PY (W)(B)/(G2PWW (B)) to obtain F = PY( S)(B)/(G2 · PW W(B)) = (G2PSS(B))/(G24kTRB) = PSS(B)/4kTRB (73.32) A better way is to input white noise W(t) in place of S(t) (a noise diode may be used). The disadvantages of noise factors are (1) when the device has low noise relative to thermal noise, the noise factor has value close to 1; (2) a low resistance causes high values; and (3) increasing the source resistance decreases the noise factor while increasing the total noise in the circuit [Ott, 1988, p. 216]. Thus, accuracy is not good. For cascaded devices, the noise factors can be conveniently computed [see Buckingham, 1985, p. 67; or Ott, 1988, p. 228]. Equivalent Input Noise Shot noise (see below) and other noise can be modeled by equivalent thermal noise that would be generated in an input resistor by increased temperature. Recall that the (maximum) incremental available power (output) in a frequency bandwidth df is PWW(df) = kTdf from Eq. (73.27). Figure 73.8(b) presents the situation. Let the resistor be the noise source at temperature To with thermal noise W(t). Then E[W(t)2 ] = 4kToRdf, by Eq. (73.24) (Nyquist’s result). Let the open circuit output noise power at RL be E[Y(t)2 ]. The incremental available noise power PYY(df) at the output (RL = R) can be considered to be due to the resistor R having a higher temperature and an ideal (noiseless) device, usually an amplifier. We must find a temperature Te at which a pseudothermal FIGURE 73.8 Equivalent input noise and noise factor