. Electronic apparatus for biological research . © Kn ^i K Figure Figure The resistance-capacitance low-pass filter—This is the arrangement of Figure By a similar process to the above Kout Vm {1 + (coCRfY'^ The moduli for the transmission factors for these two filters are plotted as functions of oj on hnear scales in Graph 8, which effectively conceals the essential symmetry in the behaviour of the two circuits. Replotting on scales of log frequency and log [transmission factor] ( a hnear scale in dB's) presents the much more satisfactory picture of Graph 9. From Graph 9 it
. Electronic apparatus for biological research . © Kn ^i K Figure Figure The resistance-capacitance low-pass filter—This is the arrangement of Figure By a similar process to the above Kout Vm {1 + (coCRfY'^ The moduli for the transmission factors for these two filters are plotted as functions of oj on hnear scales in Graph 8, which effectively conceals the essential symmetry in the behaviour of the two circuits. Replotting on scales of log frequency and log [transmission factor] ( a hnear scale in dB's) presents the much more satisfactory picture of Graph 9. From Graph 9 it is clear why the devices are called 'filters'. In the high-pass case, for example, evidently all frequencies much above co — \\CR are passed without signifi- cant attenuation, whereas all those much below \\CR are reduced. The frequency \\CR, which marks the transition between the two regimes, is called the 'turn-over frequency'; it is also sometimes, rather optimistically, called the 'cut-oflf frequency'. In general we shall call a filter any network whose transmission factor is frequency dependent. Use of log frequency and linear dB scales—The use of logarithmic scales for frequency and transmission factor (the latter is, of course, the same as saying the scale is linear in dB's) is practically universal in plotting the per- formance of all kinds of filter, for by this means the filter properties can be most clearly exhibited. In addition, the use of these scales allows the per- formance of many types of filter to be sketched freehand. For example, in the case of the R-C high-pass filter, the transmission characteristic may be sketched as follows: Mark a point, ^, at cu = \jCR, insertion loss = zero. From A, draw a dotted straight fine horizontally to the right. 35
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