RL=Load FIGURE 73.7 Measuring thermal noise voltage instantaneous velocity in a single dimension, k is Boltzmanns constant, and T is the temperature in kelvin. A shunt capacitor Cis charged by the thermal noise in the resistor [ see Fig. 73.6(b), where L is taken to be zero] The average potential energy stored is(1/2)CE[ W(()2). Equating this to 1/2kT and solving, we obtain the mean ElW(t)2]=kT/C (73.28) For example, let T= 300K and C=50 pf, and recall that k= 1.38 X 10-23J/K Then E[W(0)]=kT/C=82.8 X 10-13, so that the input rms voltage is IE[W(t112=9.09 uV. Effective noise and Antenna noise Let two series resistors R, and R2 have respective temperatures of T and t. The total noise power over an ncremental frequency band df is Pota(df)=Pi(df)+ P2(df)=4kTRdf+ 4ktRdf=4k(TR,+ tR)df. By putting TE=(T1R1+T2R2)(R1+R2) (73.29) we can write PTotal(df)=4kTE(R,+ R2)df. TE is called the effective noise temperature [see Gardner, 1990, P. 289; or Peebles, 1987, P. 228]. An antenna receives noise from various sources of electromagnetic radiation, such as radio transmissions and harmonics, switching equipment(such as computers, electrical motor controllers), thermal(blackbody) radiation of the atmosphere and other matter, solar radiation, stellar radiation, and galaxial radiation(the ambient noise of the universe). To account for noise at the antenna output, we model the noise with an equivalent thermal noise using an effective noise temperature TE. The incremental available power (output)over an incremental frequency band dfis Prr(df)=kTe df from Eq (73. 27). TE is often called antenna temperature, denoted by T. Although it varies with the frequency band, it is usually virtually constant over a small bandwidth noise Factor and noise ratio In reference to Fig. 73. 8(a), we define the noise factor F=(noise power output of actual device)/(noise power output of ideal device), where(noise power output of ideal device)=(power output due to thermal noise source) The noise source is taken to be a noisy resistor R at a temperature T, and all output noise measurements must be taken over a resistive load R, (reactance is ignored). Letting Pww(B)=4ktRB be the open circuit thermal oise power of the source resistor over a frequency bandwidth B, and noting that the gain of the device is G, the output power due to the resistive noise source becomes G Pww(B)=4kTRBG/RL. Now let Y(o be the output voltage measured at the output across Ri. Then the noise factor is e 2000 by CRC Press LLC© 2000 by CRC Press LLC instantaneous velocity in a single dimension, k is Boltzmann’s constant, and T is the temperature in kelvin. A shunt capacitor C is charged by the thermal noise in the resistor [see Fig. 73.6(b), where L is taken to be zero]. The average potential energy stored is (1/2)CE[W(t)2 ]. Equating this to 1/2kT and solving, we obtain the mean square power E[W(t)2] = kT/C (73.28) For example, let T = 300K and C = 50 pf, and recall that k = 1.38 3 10–23 J/K. Then E[W(t)2 ] = kT/C = 82.8 3 10–12, so that the input rms voltage is {E[W(t)2 ]}1/2 = 9.09 mV. Effective Noise and Antenna Noise Let two series resistors R1 and R2 have respective temperatures of T1 and T2 . The total noise power over an incremental frequency band df is PTotal(df ) = P11 (df ) + P22(df ) = 4kT1R1df + 4kT2R2df = 4k(T1R1 + T2R2 )df. By putting TE = (T1R1 + T2R2 )/(R1 + R2 ) (73.29) we can write PTotal(df ) = 4kTE (R1 + R2 )df. TE is called the effective noise temperature [see Gardner, 1990, p. 289; or Peebles, 1987, p. 228]. An antenna receives noise from various sources of electromagnetic radiation, such as radio transmissions and harmonics, switching equipment (such as computers, electrical motor controllers), thermal (blackbody) radiation of the atmosphere and other matter, solar radiation, stellar radiation, and galaxial radiation (the ambient noise of the universe). To account for noise at the antenna output, we model the noise with an equivalent thermal noise using an effective noise temperature TE . The incremental available power (output) over an incremental frequency band df is PYY (df) = kTE df, from Eq. (73.27). TE is often called antenna temperature, denoted by TA . Although it varies with the frequency band, it is usually virtually constant over a small bandwidth. Noise Factor and Noise Ratio In reference to Fig. 73.8(a), we define the noise factor F = (noise power output of actual device)/(noise power output of ideal device), where (noise power output of ideal device) = (power output due to thermal noise source). The noise source is taken to be a noisy resistor R at a temperature T, and all output noise measurements must be taken over a resistive load RL (reactance is ignored). Letting PWW (B) = 4kTRB be the open circuit thermal noise power of the source resistor over a frequency bandwidth B, and noting that the gain of the device is G, the output power due to the resistive noise source becomes G2 PWW (B) = 4kTRBG2 /RL . Now let Y(t) be the output voltage measured at the output across RL . Then the noise factor is FIGURE 73.7 Measuring thermal noise voltage