4.4 Interference Suppression and Analog Filtering

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magnitude / dB

magnitude

phase

phase / °

Fig. 4.26: Magnitude and phase frequency response of the low-pass filter from Figure 4.25: The

passband is 6 dB because of the gain by a factor of 2. The point for the cutoff frequency intersects

the 3-dB line in the segment between 700 and 800 Hz. Mathematically, the cutoff frequency is

723 Hz.

Between Ua and U2 is a non-inverting amplifier. For the voltage ratio holds:

Ua

U2

= 1 + a.

(4.11)

Between U2 and U1 there is a low pass with the transfer function

U2

U1

=

1

1 + jωRC ^.

(4.12)

Another equation is obtained by applying the node rule at U1. The sum of the three

currents flowing to this node must be zero:

U1 −Ue

R

+ ^{U1 −Ua}

1

jωC

+ ^{U1 −U2}

R

= 0.

(4.13)

Equation 4.11 to Equation 4.13 form a system of equations that can be solved for the

transmission ratio we are looking for. After calculation one obtains

Ua

Ue

=

a + 1

1 + j3ωRC −ω²R²C² −j(a + 1)ωRC ^.

(4.14)

The value a corresponds to the internal gain of the filter. This allows to realize different

filter types, i.e. filters with different slopes (cf. Table 4.4). In Figure 4.28 for the three

a-values from Table 4.4 the magnitude and phase frequency response for a 4th-order

filter are shown, which was formed from the series connection of two identical filters

according to Figure 4.27 (R1 = R2 = 10 kΩ, C1 = C2 = 22 nF). The Chebyshev filter

exhibits the steepest slope, but it also shows a characteristic ripple in the passband.

The Bessel filter has the lowest slope, but has a constant curve in the passband. All