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 • Characteristic impedance, 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 cutoff frequency 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 Inductance 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.