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When we talk about passive filters (filters that are made up of only R, L & C), we often study that the filter order will be equal to the total number of reactive components (L & C) in the circuit. Is this statement valid for all filters (low pass, high pass, band pass and band Stop)?

Circuits of band pass and band stop are a bit complex, so I wonder if this statement is also applicable to those scenarios.

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    \$\begingroup\$ No, it's overly simplistic and aimed at beginners. If you had two series inductors, that counts as two reactive components but, may not contribute any increase in the filter order. Ditto two parallel capacitors used to modify tuning to be more precise. The statement is flawed IMHO. So, where did you come across it? \$\endgroup\$
    – Andy aka
    Dec 11, 2021 at 11:38
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    \$\begingroup\$ The number of reactive components is ... the "maximum degree" of the "function"! Don't forget also the "degree" of the op-amp ... in case of active filters. \$\endgroup\$
    – Antonio51
    Dec 11, 2021 at 11:47
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    \$\begingroup\$ Try this tool ... rf-tools.com/lc-filter \$\endgroup\$
    – Antonio51
    Dec 11, 2021 at 12:08
  • \$\begingroup\$ This newbie friendly tutorial might help: (1) Butterworth Filter Design (with example on 1st to 6th order) - Electronics Tutorials, electronics-tutorials.ws/filter/filter_8.html. \$\endgroup\$
    – tlfong01
    Dec 11, 2021 at 12:20
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    \$\begingroup\$ A more accurate (though also simplistic) approach is to infer the order by measuring the steepest rate of attenuation between passband and stopband, dividing that rate by 20 (dB/decade) or 6 (dB/octave), and rounding to nearest integer. Not quite accurate for shelving filters or the highest Q filter sections but often good enough. \$\endgroup\$
    – user16324
    Dec 11, 2021 at 14:10

2 Answers 2

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The order of a circuit depends on the polynomial degree of its denominator. That degree itself depends on the number of independent state variables. State-variable are associated with energy-storing elements like \$C\$ and \$L\$ present in the circuit. So counting them seems like a good way to determine the order of the circuit.

However, I used the term independent in the above statement. It is no longer the case, for instance, if a capacitor placed across a perfect voltage source sees its voltage fixed by the source itself or when an inductor located in series with a current source has its current determined by the source. Two capacitors in parallel share a common voltage while two inductors in series share a common current. Consider the classical example described in my book on fast analytical circuits techniques or FACTs:

enter image description here

In this example, capacitor \$C_2\$ state variable \$x_2\$ is uniquely determined by the state variables \$x_1\$ and \$x_3\$. In this so-called degenerate case featuring a capacitive loop, despite the presence of 4 capacitors, it is a 3rd-order system. Add a small resistance in series with \$C_2\$ and you have a 4th-order network.

Same issue with a classical compensated divider featuring two capacitors:

enter image description here

Despite the presence of two capacitors, this is still a 1st-order system because both state variables are in a loop involving the input voltage source which fixes the potential: when you zero the voltage source to determine the poles, both capacitors are in parallel forming one capacitor only and the time constant is \$\tau=(R_1||R_2)(C_1+C_2)\$

As a conclusion, counting the energy-storing elements is the way to go but always checking that each state variable is not uniquely dependent on other state variables.

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    \$\begingroup\$ Very good example of the "compensated divider" ... Sometimes, we forget ... \$\endgroup\$
    – Antonio51
    Dec 11, 2021 at 14:37
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There is a clear definition:

The order of a filter is identical to the highest degree of the corresponding transfer function (polynominal of the numerator or denominator). However, for some good reasons, in practice the degree of the numerator polynominal will never be higher than that of the denominator. Hence, for each real and working filter, it is the denumerator (degree of the polynominal) which defines the filter order.

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