302 



BELL SYSTEM TECHNICAL JOURNAL 



Although but one source, voltmeter, and ammeter are shown, as 

 many of each as will produce distinct impedances should of course be 

 included. Multiple sources are not required because if the source 

 voltages are in defined proportions, as is necessary to determine 

 impedances independent of source voltage, the corresponding measur- 

 able admittances are linear combinations of single-source admittances, 

 by the principle of superposition; a similar requirement on source 

 currents produces impedances which are linear combinations of single- 

 source impedances. A single voltmeter is sufficient because it has no 

 effect on network currents or voltages and it is immaterial whether 



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IMPEDANCE-MEASURING EQUIPMENT SHORT-CIRCUIT LINKS 



Fig. 1. — Elements involved in impedance enumeration. 



impedances are supposed measured by successive positions of a single 

 voltmeter or by many voltmeters. The connection of an ammeter is 

 equivalent to a short circuit (except of course when in series with a 

 source) across the terminals the ammeter connects; this alters network 

 voltages and currents and the impedances measured without the 

 ammeter differ from those with it. Hence a plurality of ammeters or 

 its equivalent is required; for convenience, all ammeters except that 

 one determining a specific impedance under consideration are supposed 

 replaced by the short-circuiting links on the right of Fig. 1, thus 

 focussing attention on the single items of the enumeration. 



