Methods for the measurement of the frequency dependent complex propagation matrix, impedance matrix and admittance matrix of coupled transmission lines

A method for determining the complex frequency dependent propagation matrix, .GAMMA.(f), of a transmission line of predetermined cross section comprising:

• providing a first transmission line set of a first length l.sub..1, having said predetermined cross section;
• providing a second transmission line set of a second length l.sub.2, having said predetermined cross section;
• said first transmission line set and said second transmission line set having a first and second substantially parallel conductor and a ground conductor,
• said first conductor, said second conductor and said ground conductor forming a coupled transmission line set, each of said first conductor and said second conductor has a first and second end, said first end of said first conductor being adjacent said first end of said second conductor, said second end of said first conductor being adjacent said second end of said second conductor, at said adjacent first and second ends there being substantially uncoupled transmission line portions terminating in a first node, a second node, a third node and a fourth node;
• providing a first input pulse to said first one of said first transmission line set;
• monitoring a first plurality of outputs from said third node and said fourth node of said first transmission line set;
• providing a second input pulse to said first node of said second transmission line set;
• monitoring a second plurality of outputs from said third node and said fourth node of said second transmission line set;
• determining the complex frequency dependent Fourier transform of said first plurality of outputs at said third and fourth nodes and at said second plurality of outputs at said third and fourth nodes which are represented by:
• A.sub.3.sup.1, A.sub.3.sup.2, A.sub.4.sup.1, and A.sub.4.sup.2, respectively;
• and
• wherein said complex frequency dependent propagation matrix, .GAMMA.(f), is determined from:
• ##EQU17##

A method for determining the complex frequency dependent propagation matrix, .GAMMA.(f), of a transmission line of predetermined cross section comprising:

• providing a first transmission line set of a first length l.sub.1 having said predetermined cross section;
• providing a second transmission line set of a second length l.sub.2 having said predetermined cross section,
• said first transmission line set and said second transmission line set having a first and second substantially parallel conductor and having a ground conductor, said first conductor, said second conductor and said a ground conductor, forming a coupled transmission line, each of said first conductor and said second conductor has a first and second end, said first end of said first conductor being adjacent said fist end of said second conductor, said second end of said first conductor being adjacent said second end of said second conductor, at said second ends there being substantially uncoupled transmission line portions terminating in a third node and a fourth node, said first end of said first conductor being said first node, said first end of said second conductor being said second node;
• providing a first input pulse to said first node of said first transmission line set;
• grounding said second node of said first transmission line set;
• monitoring a first plurality of outputs from said third node and said fourth node of said first transmission line set;
• providing a second input pulse to said first node of said second transmission line set;
• grounding said second node of said second transmission line;
• monitoring a second plurality of outputs from said third node and said fourth node of said second transmission line set;
• determining the complex frequency dependent Fourier transform of said first plurality of outputs at said third and fourth nodes and of said second plurality of outputs at said third and fourth nodes which are represented by:
• A.sub.3.sup.1, A.sub.3.sup.2, A.sub.4.sup.1, and A.sub.4.sup.2, respectively;
• and
• wherein said complex frequency dependent propagation matrix, .GAMMA.(f), is determined from:
• ##EQU18##

A method for determining the complex frequency dependent propagation matrix, .GAMMA.(f), of a transmission line of predetermined cross section comprising:

• providing a first transmission line set of a first length l.sub.1 having said predetermined cross section;
• providing a second transmission line set of a second length l.sub.2 having said predetermined cross section;
• said first transmission line set and said second transmission line set having a first and second substantially parallel conductor and having a ground conductor, said first conductor, said second conductor and said a ground conductor, forming a coupled transmission line, each of said first conductor and said second conductor has a first and second end, said first end of said first conductor being adjacent said fist end of said second conductor, said second end of said first conductor being adjacent said second end of said second conductor, said first and second ends of said first conductor being a first and third node, said first and second end of said second conductor being a second and fourth node;
• providing a first input pulse to said first node of said first transmission line set;
• providing a second input pulse to said second node of said first transmission line set;
• said first and said second input pulses having substantially the same magnitude and polarity;
• monitoring a first output in response to said first and said second input pulses at said third node or said fourth node of said first transmission line set;
• providing a third input pulse to said first node of said first transmission line set;
• providing a fourth input pulse to said second node of said first transmission line set;
• said third and said fourth input pulses having substantially the same magnitude and opposite polarity;
• monitoring a second output from said third node or said fourth node of said first transmission line set;
• providing a fifth input pulse to said first node of said second transmission line set;
• providing a sixth input pulse to said second node of said second transmission line set;
• said fifth and said sixth input pulses having substantially the same magnitude and polarity;
• monitoring a third output in response to said fifth and said sixth input pulses at said third or said fourth node of said second transmission line set;
• providing a seventh input pulse to said first node of said second transmission line set;
• providing an eighth input pulse to said second node of said second transmission line set;
• said seventh and said eight input pulses having substantially the same magnitude and opposite polarity;
• monitoring a fourth output from said third node or said fourth node of said second transmission line;
• determining the complex frequency dependent Fourier transform matrices of said first output, said second output, said third output and said fourth outputs which are represented by, V.sup.1- (f), V.sup.1- (f), V.sup.2+ (f) and V.sup.2- (f) respectively;
• and
• wherein said complex frequency dependent propagation matrix, .GAMMA. (f), is determined from:
• ##EQU19##