The noise bandwidth is indicated by the vertical dashed line. Note that a significant amount of output power occurs at much higher frequency than the f3db point.įor example about 90% of the noise power appears within a frequency range up to 7xf3db. Integration of the output spectral power density from zero frequency to finite frequency f. The cumulative output power (yellow curve) at frequency f in units of V^2 is obtained by The total output RMS voltage noise is obtained by integrating the Spectral Power Density over ALL frequency and taking the square root. The blue curve is the Output Spectral Power Density Vout(f)^2 in units of V^2/Hz (the curves shown are actually normalized values). The chart below for the simple RC filter case will make the definitions clearer. Therefore the cumulative output voltage noise tends to the total output voltage noise integrated over all frequency as f ->∞ The cumulative output voltage noise at frequency f by comparison is defined as the total output voltage noise INTEGRATED OVER THE ACTUAL FILTER RESPONSE, BUT This definition of noise bandwidth also applies to the transfer function of any circuit (not just the simple passive RC filter considered here). The spectral noise power density at the output ( eth^2 in this case) gives the same noise power value as the actual total noise power at the output integrated over the filter The noise bandwidth is the number in Hz which when multiplied by the LOW frequency value of Noise voltage as would be measured with a wide-band AC voltmeter. The square root, will have a finite value because the output voltage spectral density decreases as the frequency is increased. Since this is a low-pass filter, the TOTAL thermal noise voltage, obtained by integrated the square of the output spectral noise voltage density over ALL frequency and taking The output voltage noise spectral density Vout(f) of this circuit DOES depend on frequencyĭue to the filtering action of the RC combination. The thermal noise voltage source due to the resistor R driving this simple "single pole" filter has a spectral density in V/√Hz of:Įth is independent of frequency to a very good approximation in most cases. For simplicity the simple case of the low-pass RC filter is considered with the equivalent circuit for noise shown below: This note explains the concept of "noise bandwidth".
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