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Chebyshev Filter Lowpass Prototype Element Values

Simulations of Normalized and Denormalized LP, HP, BP, and BS Filters

Prototype Lowpass Filter Schematics (Butterworth, Chebyshev, Bessel) - RF Cafe

Lowpass Filters

(above)

Highpass Filters

(above)

Bandpass and Bandstop Filters

(above)

The table below lists prototype element values for the normalized lowpass function, which assumes a cutoff frequency of 1 rad/sec and source and load impedances of 1 Ω. Either an input capacitor (top title line in table) or an input inductor (bottom title line in table) can be used. Note that for even order filters, the 0 Hz (DC) insertion loss is equal to the ripple value.

Convert values to other cutoff frequencies, impedances, and to highpass, bandpass or bandstop using denormalization equations. Complex poles are here.

Prototype filter schematic - capacitor input - RF Cafe

Capacitor Input

Prototype filter schematic - inductor input - RF Cafe

Inductor Input

* Note: In the tables below of normalized Chebyshev filter components values, the right-most column is labeled "RLoad." This is necessary because even-order Chebyshev filters are not realizable when the source and termination impedances are exactly equal. A scaling factor is included for the termination impedance as shown.

Normalized Chebyshev element values, 0.01 dB ripple*

  Capacitor Input, RS=RL=1 Ω, f=1 rad/sec
Order C1 L2 C3 L4 C5 L6 C7 L8 C9 RLoad
2 0.4489 0.4078               0.9085
3 0.6292 0.9703 0.6292             1
4 0.7129 1.2004 1.3213 0.6476           0.9085
5 0.7563 1.3049 1.5773 1.3049 0.7563         1
6 0.7814 1.3600 1.6897 1.5350 1.4970 0.7098       0.9085
7 0.7970 1.3924 1.7481 1.6331 1.7481 1.3924 0.7970     1
8 0.8073 1.4131 1.7824 1.6833 1.8529 1.6193 1.5555 0.7334   0.9085
9 0.8145 1.4271 1.8044 1.7125 1.9058 1.7125 1.8044 1.4271 0.8145 1
  L1 C2 L3 C4 L5 C6 L7 C8 L9 RLoad
  Inductor Input, RS=RL=1 Ω, f=1 rad/sec

Normalized Chebyshev element values, 0.1 dB ripple*

  Capacitor Input, RS=RL=1 Ω, f=1 rad/sec
Order C1 L2 C3 L4 C5 L6 C7 L8 C9 RLoad
2 0.8431 0.6220               0.7378
3 1.0316 1.1474 1.0316             1
4 1.1088 1.3062 1.7704 0.8181           0.7378
5 1.1468 1.3712 1.9750 1.3712 1.1468         1
6 1.1681 1.4040 2.0562 1.5171 1.9029 0.8618       0.7378
7 1.1812 1.4228 2.0967 1.5734 2.0967 1.4228 1.1812     1
8 1.1898 1.4346 2.1199 1.6010 2.1700 1.5641 1.9445 0.8778   0.7378
9 1.1957 1.4426 2.1346 1.6167 2.2054 1.6167 2.1346 1.4426 1.1957 1
  L1 C2 L3 C4 L5 C6 L7 C8 L9 RLoad
  Inductor Input, RS=RL=1 Ω, f=1 rad/sec

Normalized Chebyshev element values, 0.20 dB ripple*

  Capacitor Input, RS=RL=1 Ω, f=1 rad/sec
Order C1 L2 C3 L4 C5 L6 C7 L8 C9 RLoad
2 1.0379 0.6746               0.6499
3 1.2276 1.1525 1.2276             1
4 1.3029 1.2844 1.9762 0.8468           0.6499
5 1.3395 1.3370 2.1661 1.3370 1.3395         1
6 1.3598 1.3632 2.2395 1.4556 2.0974 0.8838       0.6499
7 1.3723 1.3782 2.2757 1.5002 2.2757 1.3782 1.3723     1
8 1.3804 1.3876 2.2964 1.5218 2.3414 1.4925 2.1349 0.8972   0.6499
9 1.3861 1.3939 2.3094 1.5340 2.3728 1.5340 2.3094 1.3939 1.3861 1
  L1 C2 L3 C4 L5 C6 L7 C8 L9 RLoad
  Inductor Input, RS=RL=1 Ω, f=1 rad/sec

Normalized Chebyshev element values, 0.5 dB ripple*

  Capacitor Input, RS=RL=1 Ω, f=1 rad/sec
Order C1 L2 C3 L4 C5 L6 C7 L8 C9 RLoad
2 1.4029 0.7071               0.5040
3 1.5963 1.0967 1.5963             1
4 1.6704 1.1926 2.3662 0.8419           0.5040
5 1.7058 1.2296 2.5409 1.2296 1.7058         1
6 1.7254 1.2478 2.6064 1.3136 2.4759 0.8696       0.5040
7 1.7373 1.2582 2.6383 1.3443 2.6383 1.2582 1.7373     1
8 1.7451 1.2647 2.6565 1.3590 2.6965 1.3389 2.5093 0.8795   0.5040
9 1.7505 1.2690 2.6678 1.3673 2.7240 1.3673 2.6678 1.2690 1.7505 1
  L1 C2 L3 C4 L5 C6 L7 C8 L9 RLoad
  Inductor Input, RS=RL=1 Ω, f=1 rad/sec
Related Pages on RF Cafe

- How to Use Filter Equations in a Spreadsheet

- Filter Transfer Functions

- Filter Equivalent Noise Bandwidth

- Filter Prototype Denormalization

- Bessel Filter Poles

- Bessel Filter Prototype Element Values

- Butterworth Lowpass Filter Poles

- Butterworth Filter Prototype Element Values

- Chebyshev Lowpass Filter Poles

- Chebyshev Filter Prototype Element Values

- Monolithic Ceramic Block Combline Bandpass

  Filters Design

- Coupled Microstrip Filters: Simple Methodologies for

  Improved Characteristics

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    BSEE - KB3UON

RF Cafe began life in 1996 as "RF Tools" in an AOL screen name web space totaling 2 MB. Its primary purpose was to provide me with ready access to commonly needed formulas and reference material while performing my work as an RF system and circuit design engineer. The World Wide Web (Internet) was largely an unknown entity at the time and bandwidth was a scarce commodity. Dial-up modems blazed along at 14.4 kbps while tying up your telephone line, and a nice lady's voice announced "You've Got Mail" when a new message arrived...

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