Elektor_Mag_-_January-February_2021

lektor January & February 2021 79

the filters had to be tuned by hand using a network analyser. There

aren’t many filter programs that can compute the complete filter.

The increasing amount of digitisation (also in video technology),

along with higher clock speeds and oversampling in DACs and

ADCs, means that there are not the same high demands on analogue

filters as there used to be. This means we can now do without the

compensation for group delay. Figure 14 shows the circuit of a

passive, second-order all-pass filter and, in Figure 15, we see the

corresponding characteristic of the group delay.

Now an excursion into practice: in Figure 16 you can see a DIY video

filter using Neosid inductors (the copper-coloured, square components

with a tuning core). The two coils on the left are part of a fifth-order

Cauer low-pass filter. The block of six coils are part of an all-pass filter.

Each time there are multiple capacitors connected in parallel in order

to realise the necessary ‘awkward’ values. The round, blue components

are KP capacitors in the nF range with a tolerance of 2%.

Unusual filters

The filters that we have discussed so far are ‘single ended’: they

operate with single-ended signals with respect to ground. But it is

also possible to build passive filters for differential signals.

Differential filters

Modern ADCs and DACs for high signal frequencies have differen-

tial inputs and outputs. It is therefore obvious that the necessary

minimum attenuation. You can see the different slopes of the

curves in the transition region and the accompanying minimum

attenuation. But this also changes the frequency of the notches.

If you would like to filter out a fixed interference frequency from a

signal, you could tune such a notch to that frequency by adjusting

the corner frequency or the minimum attenuation. With this you

have to keep a close eye on the tolerances of the components and

therefore the exact position of the notches. The enlargement of

the frequency response in Figure 11 shows that the ripple in the

pass band is 0.5 dB for all filters.

The final filter characteristic is the inverse Chebyshev (IT). This looks

like a Butterworth filter in the pass band and therefore has no ripple,

so this parameter is omitted. But in the pass band the IT characteristic

looks more like that of a Cauer filter with notches and an accompany-

ing minimum attenuation. The basic schematic is the same as that

for the Cauer filter (Figure 9) and only the dimensioning is different.

Figure 12 shows the frequency response of the inverse Chebyshev

filters with a minimum attenuation of 50, 60 and 70 dB. Figure 13 is

a zoomed-in view of the pass-band of the characteristic of Figure 12.

All-pass filters

In analogue television technology there was (once) the need for

steep filters, but the large overshoot of the step-response brought

about strong interference signals. That is why the group delay was

‘pepped up’ using all-pass filters. This took quite a bit of effort and

Figure 12: Frequency responses of the inverse Chebyshev filters with a
minimum attenuation of 50, 60 and 70 dB. The colours are self-explanatory.

Figure 13: Close-up of the pass-band of Figure 12 with a minimum

attenuation of 50 dB (blue), 60 dB (green) and 70 dB (red).

Table 1: Component values for Figure 9.

Attenuation C1 C2 C3 C4 C5 C6 C7 L1 L2 L3

40 dB 1n10 6n56 4n27 4n62 4n71 3n58 3n01 7μ90 3μ38 4μ37

50 dB 766p 4n10 2n77 4n90 5n48 4n52 3n61 8μ50 4μ78 5μ61

60 dB 541p 2n74 1n88 5n07 6n14 5n36 4n09 8μ92 6μ04 6μ65

70 dB 385p 1n90 1n31 5n20 6n68 6n07 4n45 9μ22 7μ11 7μ49