Power distribution noise

Noise distribution occurs in the active elements of electronics (bipolar transistors, electronic tubes) due to the random nature of the distribution of current between two circuits. For example, current distribution noise is present in bipolar transistors , since electric charge carriers injected from the emitter may with probability $\lambda$ ${\ displaystyle \ lambda}$ $\ lambda$ recombine in the base, and with probability $1-\lambda$ ${\ displaystyle 1- \ lambda}$ ${\ displaystyle 1- \ lambda}$ reach the collector ^[1] .

Spectral Density

Consider an electric circuit in which per unit time $n_{0}$ ${\ displaystyle n_ {0}}$ charge carriers and which are then randomly distributed between circuits $one$ ${\ displaystyle 1}$ and $2$ ${\ displaystyle 2}$ . Let the probability of the distribution of charges in the circuit $one$ ${\ displaystyle 1}$ is equal to $\lambda$ ${\ displaystyle \ lambda}$ , but in the chain $2$ ${\ displaystyle 2}$ - $1-\lambda$ ${\ displaystyle 1- \ lambda}$ . In the chain $one$ ${\ displaystyle 1}$ arrives $n1$ ${\ displaystyle n1}$ charge carriers in a circuit $2$ ${\ displaystyle 2}$ arrives $n2=n0-n1$ ${\ displaystyle n2 = n0-n1}$ charge carriers. The law of distribution of the number of current pulses in a circuit $one$ ${\ displaystyle 1}$ is binomial: $P_{n}(n_{1})={\frac {n_{0}!}{n_{1}!(n_{0}-n-{1})!}}\lambda ^{n_{1}}(1-\lambda )^{n_{0}-n_{1}}$ ${\ displaystyle P_ {n} (n_ {1}) = {\ frac {n_ {0}!} {n_ {1}! (n_ {0} -n- {1})!}} \ lambda ^ {n_ {1}} (1- \ lambda) ^ {n_ {0} -n_ {1}}}$ . For averages, we have: ${\bar {n_{1}}}=\lambda n_{0},{\bar {n_{2}}}=(1-\lambda )n_{0}$ ${\ displaystyle {\ bar {n_ {1}}} = \ lambda n_ {0}, {\ bar {n_ {2}}} = (1- \ lambda) n_ {0}}$ . For the dispersion of the number of pulses in the circuit $one$ ${\ displaystyle 1}$ we have: $\sigma _{n_{1}}={\bar {n_{1}^{2}}}-({\bar {n_{1}}})^{2}=\lambda (1-\lambda )n_{0}$ ${\ displaystyle \ sigma _ {n_ {1}} = {\ bar {n_ {1} ^ {2}}} - ({\ bar {n_ {1}}}) ^ {2} = \ lambda (1- \ lambda) n_ {0}}$ If the passage of each current pulse is associated with charge transfer $q$ ${\ displaystyle q}$ then the spectral density of the noise current distribution $i_{d}$ ${\ displaystyle i_ {d}}$ can be written as: $\sigma _{id}(\omega )=2\lambda (1-\lambda )n_{0}q^{2}\left|s_{i}^{0}(j\omega )\right|^{2}=(1-\lambda )2qI_{0}^{(1)}\left|s_{i}^{0}(j\omega )\right|^{2}$ ${\ displaystyle \ sigma _ {id} (\ omega) = 2 \ lambda (1- \ lambda) n_ {0} q ^ {2} \ left | s_ {i} ^ {0} (j \ omega) \ right | ^ {2} = (1- \ lambda) 2qI_ {0} ^ {(1)} \ left | s_ {i} ^ {0} (j \ omega) \ right | ^ {2}}$ . Here $I_{0}^{(1)}=\lambda n_{0}q$ ${\ displaystyle I_ {0} ^ {(1)} = \ lambda n_ {0} q}$ - current in the circuit $one$ ${\ displaystyle 1}$ , but $s_{i}^{0}(j\omega )$ ${\ displaystyle s_ {i} ^ {0} (j \ omega)}$ - normalized current pulse spectrum. If the current pulses associated with the motion of charge carriers in the nonequilibrium region have a duration $10^{-11}$ ${\ displaystyle 10 ^ {- 11}}$ s, then to frequency $1,6*10^{10}$ ${\ displaystyle 1.6 * 10 ^ {10}}$ Hz (centimeter waves) the noise distribution current can be considered white. In this frequency range ^[2] : $\sigma _{id}(\omega )=(1-\lambda )2qI_{0}^{(1)}$ ${\ displaystyle \ sigma _ {id} (\ omega) = (1- \ lambda) 2qI_ {0} ^ {(1)}}$

Notes

↑ Jaloud, 1977 , p. 27.
↑ Jaloud, 1977 , p. 28.

Literature

Zhalud V., Kuleshov V.N. Noises in semiconductor devices. - M .: Soviet Radio, 1977 .-- 416 p.

[_48e836dedb4eacb3-1] Jaloud, 1977 , p. 27.

[_48e836dedb4eacbc-2] Jaloud, 1977 , p. 28.

Power distribution noise

Spectral Density

Notes

Literature

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