# Noise Figure – Equivalent Noise Bandwidth

Harald Friis (Friis 1944) gave guidance on measuring the noise figure of receivers, and explains the concept of Effective Bandwidth.

#### Effective Bandwidth

The contribution to the available output noise by the Johnson-noise sources in the signal generator is readily calculated for and ideal or square-top band-pass characteristic and it is GKTB where B is the bandwidth in cycles per second. In practice, however, the band is not flat; ie, the gain over the band is not constant but varies with frequency. In this case the total contribution is ∫GfKTdf where Gf is the gain at frequency f. The effective bandwidth B of the network is defined as the bandwidth of an ideal band-pass network with gain G that gives this contribution to the noise output.

Above is the response of the ‘factory’ 2400Hz soft filter in an IC-7300 (SDR) transceiver. It is not an ideal rectangular response.

To perform the calculation described by Friis, ∫GfKTdf, we firstly need a G(f) dataset. The above plot is of the log of G(f) and to perform geometric operations to find the area under the curve is quite misguided.

Above is a plot of G(f) (measured with Gaussian noise integrated over a period), and we can find ∫GfKTdf wrt G at some reference frequency (1kHz in the above example as that is what is used for sensitivity measurement).

In this case the filter -6dB response is 377-2616Hz=2239Hz, and Effective Bandwidth wrt gain at 1kHz is 2077Hz.

In my own articles and software I usually refer to this as the Equivalent Noise Bandwidth (ENB) to be clearer.

ARRL to be different refer to Equivalent Rectangular Bandwidth but they do not expose how they calculate it (it is a hammy thing).

The term Equivalent Noise Bandwidth is sometimes used.