Journal of Electrical and Computer Engineering

Research Article

The Generalization of the Extra Element Theorem for Symbolic Circuit Tolerance Analysis

Table 1

The elements parameters of the transistor amplifier shown in Figure 2 and the results of tolerance analysis.
𝜒 𝑖 Symbolic expressions of network determinants 𝑁 𝜒 and 𝐷 𝜒 𝛾 % 𝛿 ( 𝜒 𝑖 ) %
𝛿 ( 𝜒 𝑖 ) = + 1 0 % 𝛿 ( 𝜒 𝑖 ) = − 1 0 % 𝛾 = + 1 5 % 𝛾 = − 1 5 %
𝑅 1 10 kΩ 𝑁 𝜒 = 𝑅 6 𝐵 2 𝑅 3 𝐵 1 = 1 0 0 0 0 0 0 0 0 0 0 ;
𝐷 𝜒 = ( 𝐵 1 𝑅 2 + 𝑅 2 + 𝑅 5 ) ( 𝑅 3 + 𝑅 4 ) = 2 2 2 0 0 0 0 0 		8−8.319−18
𝑅 2 0.1 kΩ 𝑁 𝜒 = 𝑅 6 ( ( 𝑅 3 + 𝑅 4 ) ( 𝐵 1 + 1 ) + ( − 𝐵 2 𝑅 3 ) ( − 𝐵 1 ) )
    = 1 0 2 0 2 0 0 0 0 0 0 ;
𝐷 𝜒 = ( 𝑅 3 + 𝑅 4 ) ( 𝐵 1 𝑅 1 + 𝑅 1 + 𝑅 5 ) + ( ( 𝑅 3 + 𝑅 4 ) 𝑅 6 ) ( 𝐵 1 + 1 )
   + ( − 𝑅 3 𝑅 6 𝐵 2 ) ( − 𝐵 1 ) = 1 2 2 2 4 0 0 0 0 0 0 		−8.910.8−13.418
𝑅 3 1 kΩ 𝑁 𝜒 = 𝑅 6 ( ( 𝑅 2 ( 𝐵 1 + 1 ) ) + ( − 𝐵 2 ) ( − 𝐵 1 ( 𝑅 1 + 𝑅 2 ) ) )
    = 1 0 1 0 1 0 1 0 0 0 0 0 ; 𝐷 𝜒 = ( 𝐵 1 𝑅 1 𝑅 2 + 𝑅 1 ( 𝑅 2 + 𝑅 5 ) + 𝑅 2 𝑅 5 )
   + ( 𝑅 6 ) ( 𝐵 1 𝑅 2 + 𝑅 2 + 𝑅 5 ) + ( − 𝑅 6 𝐵 2 ) ( − 𝑅 2 𝐵 1 )
    = 1 1 2 2 2 0 0 0 0 0 		0.89−1.1−403−64
𝑅 4 1 kΩ 𝑁 𝜒 = 𝑅 6 𝑅 2 ( 𝐵 1 + 1 ) = 1 0 1 0 0 0 0 0 ; 𝐷 𝜒 = 𝐵 1 ( 𝑅 1 + 𝑅 6 ) 𝑅 2 + ( 𝑅 1 + 𝑅 6 ) ( 𝑅 2 + 𝑅 5 ) + 𝑅 2 𝑅 5
    = 1 2 2 2 0 0 0 0 0 		−0.970.99−133180
𝑅 5 1 kΩ 𝑁 𝜒 = 0 ; 𝐷 𝜒 = ( 𝑅 1 + 𝑅 2 + 𝑅 6 ) ( ( 𝑅 3 + 𝑅 4 ) ) = 2 2 2 0 0 0 0 0 −0.170.17−731989
𝑅 6 1 kΩ 𝑁 𝜒 = ( 𝑅 3 + 𝑅 4 ) ( 𝑅 2 ( 𝐵 1 + 1 ) ) + ( − 𝐵 2 𝑅 3 ) ( − 𝐵 1 ( 𝑅 1 + 𝑅 2 ) )
    = 1 0 1 0 2 0 2 0 0 0 0 0 ;
𝐷 𝜒 = ( 𝑅 3 + 𝑅 4 ) ( 𝐵 1 𝑅 2 + 𝑅 2 + 𝑅 5 ) + ( − 𝐵 2 𝑅 3 ) ( − 𝑅 2 𝐵 1 )
    = 1 0 2 2 2 0 0 0 0 0 		1.7−1.9271−49.7
𝐵 1 100 S 𝑁 𝜒 = 𝑅 6 ( 𝐵 2 𝑅 3 ( 𝑅 1 + 𝑅 2 ) + 𝑅 2 ( 𝑅 3 + 𝑅 4 ) )
    = 1 0 1 0 2 0 0 0 0 0 0 0 0 ; 𝐷 𝜒 = 𝑅 2 ( 𝑅 6 𝐵 2 𝑅 3 + ( 𝑅 1 + 𝑅 6 ) ( 𝑅 3 + 𝑅 4 ) )
    = 1 2 2 0 0 0 0 0 0 0 0 		0.17−0.21−117−90
𝐵 2 100 S 𝑁 𝜒 = 𝑅 6 𝑅 3 𝐵 1 ( 𝑅 1 + 𝑅 2 ) = 1 0 1 0 0 0 0 0 0 0 0 0 0 ;
𝐷 𝜒 = 𝑅 6 𝑅 2 𝐵 1 𝑅 3 = 1 0 0 0 0 0 0 0 0 0 0 		1.8−2.1198−47