Conditions For Driving Point Function:

The restrictions on pole and zero locations in the Conditions For Driving Point Function with common factors in P(s) and Q(s) cancelled are listed below.

1. The coefficients in the polynomials P(s) and Q(s) of network function N(s) = P(s)/Q(s) must be real and positive.

2. Complex poles or imaginary poles and zeros must occur in conjugate pairs.

3. (a) The real parts of all poles and zeros must be zero, or negative. (b) If the real part is zero, then the pole and zero must be simple.

4. The polynomials P(s) and Q(s) may not have any missing terms between the highest and the lowest degrees, unless all even or all odd terms are missing.

5. The degree of P(s) and Q(s) may differ by zero, or one only.

6. The lowest degree in P(s) and Q(s) may differ in degree by at the most one.

Necessary Conditions for Transfer Functions:

The restrictions on pole and zero location in transfer functions with common factors in P(s) and Q(s) cancelled are listed below.

1. (a) The coefficients in the polynomials P(s) and Q(s) of N(s)=P(s)/Q(s) must be real. (b) The coefficients in Q(s) must be positive, but some of the coefficients in P(s) may be negative.

2. Complex or imaginary poles and zeros must occur in conjugate pairs.

3. The real part of poles must be negative, or zero. If the real part is zero, then the pole must be simple.

4. The polynomial Q(s) may not have any missing terms between the highest and the lowest degree, unless all even or all odd terms are missing.

5. The polynomial P(s) may have missing terms between the lowest and the highest degree.

6. The degree of P(s) may be as small as zero, independent of the degree of Q(s).

7. (a) For the voltage transfer ratio and the current transfer ratio, the maximum degree of P (s) must equal the degree of Q(s). (b) For transfer impedance and transfer admittance, the maximum degree of P (s) must equal the degree of Q(s) plus one.

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