Page 135 - Analog and Digital Filter Design

1 32 Analog and Digital Filter Design

handle mains current these inductors tend to have low values of differential
inductance and are physically quite large.

Most mains filters use so-called “Y capacitors” connected between earth and
the go and return wires. These Y capacitors typically have values of around a
few nano-farad (larger values would exceed earth leakage limits imposed by the
relevant safety authorities).

The earth leakage limits imposed on medical equipment, especially if patient-
connected, usually makes it impossible to use any reasonable size of Y capaci-
tor. Instead, such filters have to use better inductors and more filter stages. To
avoid this large and costly filter, the patient-connected end of the equipment is
often made battery-powered and communicates with the mains-powered equip-
ment through an electrically isolated path, such as an opto-coupler or fiber optic
link.

Active Lowpass Filters

In Chapter 3, 1 stated that active filters are designed using pole and zero loca-
tions, which are determined from the frequency response’s transfer function.
This is not possible in passive filter designs because all the components interact
with each other. However, in active filters the operational amplifier (op-amp),
the “active” part of the circuit, buffers one stage from the next so there is no
interaction. Each stage can therefore be designed to provide the frequency
response of one pair of complex poles, or a single real pole, or sometimes both.
When all the stages are connected in series, the desired overall response is
produced.

Now that I have set the scene, I will describe some active filter designs and see
how the pole and zero locations are used to find component values.

First-Order Filter Section

The first-order section is a simple structure comprising a lowpass RC network,
followed by a buffer, as shown in Figure 4.9. The buffer serves to provide a high
input impedance, so that the voltage at the connection node of the RC network
is transferred to the buffer’s output without being loaded by following stages. A
simple RC network on its own would be loaded by following stages and there-
fore not have the expected frequency response.

The first-order section is an all-pole network, because it cannot produce zeroes
in its frequency response. In fact, the first-order section has one real pole at -a