noise power E[W (02]=4kT Rdf yields the extra"input"noise power. Let V(n)=w(r)+ w(r). Then Pw(df 4kTRdf+ 4kT Rdf=4k(T+ T)RdfW, from Eq (73.24). T is called the equivalent input noise temperature. It related to the noise factor F by T:=290(F-1). In cascaded amplifiers with gains G,, G2,... and equivalent the total equivalent input noise temperature is Te(Total)=Tel T2/G1+ T3/GG+ (73.33) [see Gardner, 1990, P. 289] Other electrical noise Thermal noise and shot noise(which can be modeled by thermal noise with equivalent input noise)are the main noise sources. Other noises are discussed in the following paragraphs. Shot noise In a conductor under an external emf, there is an average flow of electrons, holes, photons, etc. In addition this induced net flow and thermal noise, there is another effect. The potential differs across the boundaries of metallic grains and particles of impurities, and when the kinetic energy of electrons exceeds electrons jump across the barrier. This summed random flow is known as shot noise[see Gardner, 1990, P. 239 Ott, 1988, P. 208. The shot effect was analyzed by Schottky in 1918 as Ih=(2qLd b)n, where q=1.6X 10-19 oulombs per electron, Idc average dc current in amperes, and B=noise bandwidth(Hz) Partition noise Partition noise is caused by a parting of the flow of electrons to different electrodes into streams of randomly varying density. Suppose that electrons from some source S flow to destination electrodes A and B. Let n(A) and n( B) be the average numbers of electrons per second that go to nodes A and B respectively, so that n(S) n(A)+n(B)is the average total number of electrons emitted per second. It is a success when an electron goes to A, and the probability of success on a single trial is P, where P=n(A)/n(S),1-p=n(B)/n(S) (73.34) The current to the respective destinations is I(A)=n(A)a, I(B)=n(B)a, where q is the charge of an electron, that I(A)I(S)=pand I(B)/I(S=l-P. Using the binomial model, the average numbers of successes are E[n(A)]=n(S)p and E[n(B)]=n(S)(1-P). The variance is Var(n(A))=n(S)p(1-P)=Var(n(B))(from the binomial formula for variance). Therefore, substitution yields Var(I(A))=q[n(S)p(I-p)]= gn(S)I(A)I(B)/[I(A)+I(B) 73.35) Partition noise applies to pentodes, where the source is the cathode, A is the anode(success), and B is the grid. For transistors, the source is the emitter, A is the collector, and B represents recombination in the bas In photo devices, a photoelectron is absorbed, and either an electron is emitted (a success)or not. Even a partially silvered mirror can be considered to be a partitioner: the passing of a photon is a success and reflection is a failure. While the binomial model applies to partitions with destinations A and B, multinomial models are analogous for more than two destinations. Flicker, Contact, and Burst Noise B. Johnson first noticed in 1925 that noise across thermionic gates exceeded the expected shot noise at lower frequencies. It is most noticeable up to about 2 kHz. The psdf of the extra noise, called flicker noise, is S(刀)=P/axf,f>0 (73.36) where I is the dc current flowing through the device and fis the positive frequency. Empirical values of a are about 1 to 1.6 for different sources. These sources vary but include the irregularity of the size of macro regions e 2000 by CRC Press LLC© 2000 by CRC Press LLC noise power E[We (t)2 ] = 4kTeRdf yields the extra “input” noise power. Let V(t) = W(t) + We(t). Then PVV (df) = 4kToRdf + 4kTeRdf = 4k(To + Te)Rdf W, from Eq. (73.24). Te is called the equivalent input noise temperature. It is related to the noise factor F by Te = 290(F – 1). In cascaded amplifiers with gains G1, G2 , . . . and equivalent input noise temperatures Te1 , Te2 , . . ., the total equivalent input noise temperature is Te(Total) = Te1 + Te2 /G1 + Te3 /G1G2 + . . . (73.33) [see Gardner, 1990, p. 289]. Other Electrical Noise Thermal noise and shot noise (which can be modeled by thermal noise with equivalent input noise) are the main noise sources. Other noises are discussed in the following paragraphs. Shot Noise In a conductor under an external emf, there is an average flow of electrons, holes, photons, etc. In addition to this induced net flow and thermal noise, there is another effect. The potential differs across the boundaries of metallic grains and particles of impurities, and when the kinetic energy of electrons exceeds this potential, electrons jump across the barrier. This summed random flow is known as shot noise [see Gardner, 1990, p. 239; Ott, 1988, p. 208]. The shot effect was analyzed by Schottky in 1918 as Ish = (2qIdcB)1/2, where q = 1.6 3 10–19 coulombs per electron, Idc = average dc current in amperes, and B = noise bandwidth (Hz). Partition Noise Partition noise is caused by a parting of the flow of electrons to different electrodes into streams of randomly varying density. Suppose that electrons from some source S flow to destination electrodes A and B. Let n(A) and n(B) be the average numbers of electrons per second that go to nodes A and B respectively, so that n(S) = n(A) + n(B) is the average total number of electrons emitted per second. It is a success when an electron goes to A, and the probability of success on a single trial is p, where p = n(A)/n(S), 1 – p = n(B)/n(S) (73.34) The current to the respective destinations is I(A) = n(A)q, I(B) = n(B)q, where q is the charge of an electron, so that I(A)/I(S) = p and I(B)/I(S) = 1 – p. Using the binomial model, the average numbers of successes are E[n(A)] = n(S)p and E[n(B)] = n(S)(1 – p). The variance is Var(n(A)) = n(S)p(1 – p) = Var(n(B)) (from the binomial formula for variance). Therefore, substitution yields Var(I(A)) = q2[n(S)p(1 – p)] = q2n(S){I(A)I(B)/[I(A) + I(B)]} (73.35) Partition noise applies to pentodes, where the source is the cathode, A is the anode (success), and B is the grid. For transistors, the source is the emitter, A is the collector, and B represents recombination in the base. In photo devices, a photoelectron is absorbed, and either an electron is emitted (a success) or not. Even a partially silvered mirror can be considered to be a partitioner: the passing of a photon is a success and reflection is a failure. While the binomial model applies to partitions with destinations A and B, multinomial models are analogous for more than two destinations. Flicker, Contact, and Burst Noise J.B. Johnson first noticed in 1925 that noise across thermionic gates exceeded the expected shot noise at lower frequencies. It is most noticeable up to about 2 kHz. The psdf of the extra noise, called flicker noise, is S(f) = I2/af, f > 0 (73.36) where I is the dc current flowing through the device and f is the positive frequency. Empirical values of a are about 1 to 1.6 for different sources. These sources vary but include the irregularity of the size of macro regions