Constraint on Thevenin impedance

[PatrickCummin]

Let's say we have a circuit composed of simple linear circuit elements (resistors, inductors and capacitors). Now we calculate the Thevenin equivalent circuit for some load within this circuit, and we determine the Thevenin impedance, Z_t.

My question is this: Is it generally the case that the real part of Z_t is positive (Re Z_t greater than or equal to zero)? In particular, has this been proven to be generally the case?

Thanks for any help, Patrick

 

[jsgruszynski]

You want to look at linear algebra to answer this.

Specifically how
http://en.wikipedia.org/wiki/Equiva...inal.2C_n-element.2C_3-element-kind_networks" impedance matrices.

Also think about what driving-point impedance and Thevenin/Norton reduction actually means in the context of an impedance matrix with I and V vectors.

 

[uart]

Let's say we have a circuit composed of simple linear circuit elements (resistors, inductors and capacitors). Now we calculate the Thevenin equivalent circuit for some load within this circuit, and we determine the Thevenin impedance, Z_t.

My question is this: Is it generally the case that the real part of Z_t is positive (Re Z_t greater than or equal to zero)? In particular, has this been proven to be generally the case?

Thanks for any help, Patrick

Hi Patrick. The simple answer is that for linear circuits containing only independent sources then yes the real part of the Thevenin impedance is non-negative. However for circuits containing dependent sources the Thevenin resistance may be negative.