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This describes how the capacitance of coaxial audio cable influences the performance of an audio system as it pertains to connections between line output levels and unbalanced line input (as in to a sound-card). In summary, this situation produces a pole which yields a high frequency roll-off above it's corner frequency. This is a quick analysis of the first order effect involved.
Examples of line level outputs would be things like mic mixers, mic pre-amps, tape deck outputs, phone pre-amp outputs and so on. The example that I will use involve the following assumptions:
1. Coaxial cable has between 15 to 25 pF / foot (picofarad per foot). I will use the middle value of 20 pF / foot.
2. The output driving point resistance of the source is 600 Ohms resistive
3. The input resistance of the receiving device is 50K Ohms resistive
4. The inductance of the cable is negligible at audio frequencies beyond the audio spectrum and up to several MHz.
5. The characteristic impedance of the coaxial cable is of no relevance at these frequencies and distances since the wavelength of audio is very long comparatively.
6. The run distance between the source device and the receiving device will be 10 feet.
7. The electrical resistance of the cable is negligible compared to the input resistance of the receiving device (usually a sound card input)
8. The evaluation is for line-level circuits.
Since the input resistance of our theoretical receiver is much higher than the output resistance of the transmitter, the Thevenin equivalent resistance of the circuit can be assumed to be totally dominated by the source resistance. The corner frequency (-3dB point on the attenuation curve) will simply be:
F (-3dB) = 1 / (2π R x C)
Wherein C = total cable capacitance in Farads, R = driving point resistance of source in Ohms, and F is frequency in Hz
Thus, with a 10 foot run of audio coax between the two devices, the total cable capacitance will be 20 pf x 10 = 200 pF (200 x 10 x-12 Farads)
So, the corner frequency of this signal pathway will be
1.33 MHz (1.33 Mega Hertz)
Put another way, one would have to create a very long run between the source and the receiver (~500 feet) using the above assumptions to create a -3dB corner frequency @27 kHz due to the coaxial cable. Other issues like ground loops and "H" fields would come more into play at that distance, both of which can be alleviated by using a balanced system.
Conclusion - since the audio spectrum runs from 20 Hz to 20 kHz (20 Kilo Hertz), the cable capacitance will have no impact on signal loss on short runs. The dominant pole in these situations will be internal compensation of the source or the roll-off characteristics of the receiver.
Craig
Examples of line level outputs would be things like mic mixers, mic pre-amps, tape deck outputs, phone pre-amp outputs and so on. The example that I will use involve the following assumptions:
1. Coaxial cable has between 15 to 25 pF / foot (picofarad per foot). I will use the middle value of 20 pF / foot.
2. The output driving point resistance of the source is 600 Ohms resistive
3. The input resistance of the receiving device is 50K Ohms resistive
4. The inductance of the cable is negligible at audio frequencies beyond the audio spectrum and up to several MHz.
5. The characteristic impedance of the coaxial cable is of no relevance at these frequencies and distances since the wavelength of audio is very long comparatively.
6. The run distance between the source device and the receiving device will be 10 feet.
7. The electrical resistance of the cable is negligible compared to the input resistance of the receiving device (usually a sound card input)
8. The evaluation is for line-level circuits.
Since the input resistance of our theoretical receiver is much higher than the output resistance of the transmitter, the Thevenin equivalent resistance of the circuit can be assumed to be totally dominated by the source resistance. The corner frequency (-3dB point on the attenuation curve) will simply be:
F (-3dB) = 1 / (2π R x C)
Wherein C = total cable capacitance in Farads, R = driving point resistance of source in Ohms, and F is frequency in Hz
Thus, with a 10 foot run of audio coax between the two devices, the total cable capacitance will be 20 pf x 10 = 200 pF (200 x 10 x-12 Farads)
So, the corner frequency of this signal pathway will be
1.33 MHz (1.33 Mega Hertz)
Put another way, one would have to create a very long run between the source and the receiver (~500 feet) using the above assumptions to create a -3dB corner frequency @27 kHz due to the coaxial cable. Other issues like ground loops and "H" fields would come more into play at that distance, both of which can be alleviated by using a balanced system.
Conclusion - since the audio spectrum runs from 20 Hz to 20 kHz (20 Kilo Hertz), the cable capacitance will have no impact on signal loss on short runs. The dominant pole in these situations will be internal compensation of the source or the roll-off characteristics of the receiver.
Craig