Hi,
As mentioned before, the chracteristic impedance of a cable is sqrt(L/C), where L and C are the inductance and capacitance per unit length (assuming perfect conductors and no leakage across the dielectric). Characteristic impedance is a property intrinsic to the cable, not affected by external components such as resistors or input impedances of an amplifier.
The characteristic impedance of cables and connectors relates the voltage wave to the current wave (or equivalently the electric fields and magnetic fields) flowing along the wire. Thus for an infinitely long cable with characteristic impedance of 50 ohms, if a voltage pulse is sent down with amplitude V, the current pulse will have magnitude V/50.
Even if there is a change in impedance (such as being driven by an amplifier - zero impedance, or connecting to a high impedance input), the voltage and current waves must still obey this relationship within the cable - there will be voltage/current reflections when there is a change in impedance to ensure the relationship holds true. For a cable of given length, these reflections will cause peaks and nodes in the frequency response. At low frequencies, there is little effect and one is oblivious to the reflections because the signal is much slower than the propagation delay. For fast signals such as digital and video, there can be problems, especially for long cable runs.
By terminating a cable with a resistor equal to its characteristic impedance, there will be no reflections, so signal quality is preserved (the resistor looks like an infinite length of the cable). That is why on high frequency oscilloscopes you see one of the input options is 50 ohms.
This is why RCA connectors are actually unsuitable for digital signals and video - because of the impedance change from the ~50 ohm coax to the ~25 ohm connector. Out of interest, twisted pair cables have a characteristic impedance of ~100 ohms.
Having a certain input impedance to an amplifier has nothing to do with the cable - you won't find many (AF) amplifiers with input impedances around 50 ohms!
Hope this helps,
Chris.
As mentioned before, the chracteristic impedance of a cable is sqrt(L/C), where L and C are the inductance and capacitance per unit length (assuming perfect conductors and no leakage across the dielectric). Characteristic impedance is a property intrinsic to the cable, not affected by external components such as resistors or input impedances of an amplifier.
The characteristic impedance of cables and connectors relates the voltage wave to the current wave (or equivalently the electric fields and magnetic fields) flowing along the wire. Thus for an infinitely long cable with characteristic impedance of 50 ohms, if a voltage pulse is sent down with amplitude V, the current pulse will have magnitude V/50.
Even if there is a change in impedance (such as being driven by an amplifier - zero impedance, or connecting to a high impedance input), the voltage and current waves must still obey this relationship within the cable - there will be voltage/current reflections when there is a change in impedance to ensure the relationship holds true. For a cable of given length, these reflections will cause peaks and nodes in the frequency response. At low frequencies, there is little effect and one is oblivious to the reflections because the signal is much slower than the propagation delay. For fast signals such as digital and video, there can be problems, especially for long cable runs.
By terminating a cable with a resistor equal to its characteristic impedance, there will be no reflections, so signal quality is preserved (the resistor looks like an infinite length of the cable). That is why on high frequency oscilloscopes you see one of the input options is 50 ohms.
This is why RCA connectors are actually unsuitable for digital signals and video - because of the impedance change from the ~50 ohm coax to the ~25 ohm connector. Out of interest, twisted pair cables have a characteristic impedance of ~100 ohms.
Having a certain input impedance to an amplifier has nothing to do with the cable - you won't find many (AF) amplifiers with input impedances around 50 ohms!
Hope this helps,
Chris.