Elektor_Mag_-_January-February_2021

76 January & February 2021 http://www.elektormagazine.com

Now that we are on the subject of impedances we can also take

a look at the effect an incorrect source or load resistance has. As

an example we connect a filter that has been dimensioned for an

impedance of 100 Ω to a source with a 50 Ω impedance. It is also

terminated at the output with a 50 Ω impedance. Figure 6 shows

the frequency characteristic in the pass band.

Returning to the topic of dimensioning, with a Chebyshev filter

the ripple in the pass-band is an additional parameter. The effect

on the frequency response can be seen in Figure 7. Here we see

the amplitude responses of a seventh-order 1 MHz Chebyshev

low-pass with a ripple of 0.1 dB, 0.5 dB, 1 dB and 3 dB in the

pass-band. The more ripple allowed, the steeper the curve in

is proportional to 1 / √(L * C). That is why, in the era before pocket
calculators and PCs, it was easy to convert a basic schematic with
a given corner frequency to the desired design frequency. If the
standard impedance of 50 Ω remains the same then the resistor
values, of course, also remain the same.

It is also interesting to see how the component values behave when
a filter is redimensioned for other impedances. This is also possi-
ble without the help of a computer. If we would like to double the
impedances in the 1 MHz low-pass filter in Figure 5 from 50 Ω
to 100 Ω then we only have to double the values of the inductors
and halve the values of the capacitors. Again, this is not a surprise,
because Z is proportional to √(L/C).

L5

R 1 C 1

L6 R 2

C 2

C 5 C 6

7. Order

BS Shunt First BS Series First

L1 L2

L7

C 3

C 7

C 4

L3 L4

L2

R 1 C 5

L3 R 2

C 6

C 2 C 3

L5 L6

L4

C 7

C 4

L7

L1

C 1

L4

R 1 C 1

L5 R 2

C 2

C 4 C 5

L1 L2

C 3

L2

R 1 C 4

L3 R 2

C 5

C 2 C 3

L4 L5

L1

C 1

L3

R 1 C 1

R 2

C 2

C 3

L1 L2

L2

R 1 C 3

R 2

C 2

L3

L1

C 1

5. Order


6. Order

L2

L5

R 1 C 1

C 5 R 2

L1 L2 C 2

L6 C 6

L3 C 3

L7 C 7

L4 C 4

L1

R 1

C 1 R 2

C 5

L5

C 2 L2

C 6

L6

C 3 L3

C 7

L7

C 4 L4

7. Order

L4

R 1 C 1

C 4 R 2

L1 L2 C 2

L5 C 5

L3 C 3

L1

R 1

C 1 R 2

C 4

L4

C 2 L2

C 5

L5

C 3 L3

L3

R 1 C 1

C 3 R 2

L1 L2 C 2

L1

R 1

C 1 R 2

C 3

L3

C 2 L2

5. Order


6. Order

BP Shunt First BP Series First

200522-003b

200522-003a

Figure 3: Basic schematics for band-pass filters and band-stop filters of third, fifth and seventh order with Bessel, Butterworth or Chebyshev characteristics
using PI and T structures.