Constant k High Pass Filter

Presentation by: S.KARTHIE Assistant Professor/ECE SSN College of Engineering Objective

At the end of this section students will be able to understand,

• What is a constant k high pass filter section

• , attenuation and phase constant of high pass filters.

• Design equations of high pass filters. High Pass Ladder Networks

• A high-pass network arranged as a ladder is shown below. • As mentioned earlier, the repetitive network may be considered as a number of T or ∏ sections in cascade . C C C CC

LL L L High Pass Ladder Networks

• A T section may be taken from the ladder by removing ABED, producing the high-pass filter section as shown below.

AB C CC 2C 2C 2C 2C

LL L L

D E High Pass Ladder Networks • Similarly, a ∏ section may be taken from the ladder by removing FGHI, producing the high- pass filter section as shown below.

F G CCC

2L 2L 2L 2L

I H Constant- K High Pass Filter

• Constant k HPF is obtained by interchanging Z 1 and Z 2. 1 Z1 === & Z 2 === jωωωL jωωωC

L 2 • Also, Z 1 Z 2 ======R k is satisfied. C Constant- K High Pass Filter

• The HPF filter sections are

2C 2C C

L 2L 2L Constant- K High Pass Filter Reactance curve X

Z2

fC f Z1

Z1= -4Z 2

Stopband Passband Constant- K High Pass Filter

• The is 1 fC === 4πππ LC

• The characteristic impedance of T and ∏ high pass filters sections are

R k 2 Oπππ fC Z === ZOT === R k 1 −−− f 2 f 2 1 −−− C f 2 Constant- K High Pass Filter Characteristic impedance curves

ZO

ZOπ

Nominal R k Impedance

ZOT

fC Frequency Stopband Passband Constant- K High Pass Filter • The attenuation and phase constants are

 fC   fC  ααα === 2cosh −−−1   βββ === −−− 2sin −−−1    f   f  f C f f ααα

−−−πππ

f C f βββ f Constant- K High Pass Filter

Design equations • The expression for and Capacitance is obtained using cutoff frequency.

R k 1 L === C === 4πππfC 4πππR k fC

1 fC === 4πππ LC Summary

• A Ladder networks consisting of opposite type impedances and which satisfy the relationship

2 Z 0T Z 0πππ === Z1Z 2 === R k === 'Cons tan t 'k

is called constant k filter sections.

• The characteristic impedance of a filter is purely resistive in the passband which equal to L ZOT === R k === C this value of characteristic impedance is called nominal or design impedance of the network. Summary

• The cutoff frequency of a filter is obtained using relation

Z1 === −−−4Z2

• The cutoff frequencies of a T and ∏ networks is same. Hence these networks are called prototypes . Thank You