Switching System Bandwidth and Impedance
When measuring the bandwidth of a switching system the test equipment used is usually based on 50Ohm measurements (if they are 75Ohm they are specifically stated, typically these will be for applications for broadcasting and cable TV systems).
In reality this is not a common impedance used for higher voltage or non RF systems, so we do get asked what impact scaling the impedance has.
Scaling For Impedance
For a system where the main BW limitation is capacitance (usually the case in non RF designs such as crosspoint matrices and non tree multiplexers) and some simple guidance can be given.
As the impedance of the source and the load are both scaled up from 50Ohm the capacitance will have a progressively greater impact.
So for a 50Ohm source and load with a design having 5MHz BW then increasing the source and load impedance to 500Ohms will reduce the BW by a factor of ten to 500kHz, increasing to 5kOhm source and load will reduce the BW to 50kHz.
This guidance does not work in all cases, for example in RF designs matching circuits might not scale in quite this way. If the source impedance is kept low then the BW is much less impacted since the capacitance to ground is working against a single 50Ohm resistor rather than two 50Ohm resistors.
Effect of Non RF Cables
External cables can also add to the capacitance seen and have an impact on the bandwidth observed, cables have a characteristic impedance typically in the range 50Ohm to 120Ohm so once the source and load impedance is above this impedance they appear predominantly as additional capacitance to ground. Similarly if the source impedance is below the cable connection impedance the cable may appears inductive.
Estimate Capacitance from Bandwidth
Where a low frequency (non-RF) switching system has bandwidth information the excess input capacitance can be estimated from calculating the value of capacitance by using the 50 Ohm bandwidth and calculating the value of capacitance that is approximately 25 Ohms at that 3dB bandwidth frequency. This can be useful when there is interest in knowing the AC leakage current that a switching system (and cables) creates by capacitive loading on AC sources. This does not work for RF designs.
