A simple mathematical model for attenuated HBC channel

It has been proven widely and largely by a number of researchers that human body is essentially an attenuated transmission channel. This means that this attenuated channel could be modeled as a deterministic linear time-invariant filter with impulse response h(t) as shown in the figure below.

In this case h(t) could be represented as,

H(f) is the fourier transform of h(t) expressed as,

In this figure s(t) is the transmitted signal, w(t) represents additive white gaussian noise and z(t) is the convolution of s(t) with h(t).

In frequency domain, fourier transform Z(f) of z(t) is given by,

 So r(t) is given by,

If  is very small then signal z(t) would be very weak as compared to noise and interference represented by w(t). This will reduce performance of the receiver and because of this reason communication distance could also not be very large between transmitter and receiver.

This derivation has been adopted from "Introduction to Digital Communications" compendium written by Göran Lindell, LTH, Lund University.

60-Hz power line interference with human body

60-Hz power line interference could either couple through electromagnetic induction or through electrostatic induction to the underlying circuit.

 

Electromagnetic Induction

The magnetic field due to mains supply current induces electromotive force (emf) in the electrodes, associated lead wires and preamplifier of the BAN trannsceiver. The greater the loop area covered by the mains supply current, the larger is the value of induced emf. However when the same electrodes, lead wires and preamplifier are worn on the body, there is very little amount of induced emf in the receiver due to much lesser loop area.

 

Electrostatic Induction

In case of electrostatic induction, the mains supply current gets capacitively coupled to the human body. The body-to-ground capacitance plays an important role in introducing interference as the pre-amplifier is also isolated from true earth or gound in battery held devices. A displacement current therefore flows through the human body which produces common mode voltage at the electrodes with respect to ground. 

It is assumed that electrostatic induction is the dominant form of interference for BAN transceiver rather than electromagnetic induction.