The Insertion Loss Method of Lumped Element Filter Design

Key Takeaways

• When filters are realized using passive devices smaller than the circuit operating wavelength, lumped element filters are formed. 

• Lumped element filters possess advantages such as lower costs, a smaller footprint, and a wider bandwidth than their distributed element counterparts. There is only a minimal phase shift between the input and output waveforms in lumped element filters.

• The insertion loss method introduces network synthesis techniques to design filters with desirable characteristics. Design procedures include low-pass filter prototypes that are normalized in terms of impedance and frequency. Transformations are applied to the low-pass filter prototype to achieve the final filter design. 

Filters are indispensable in any RF/microwave system, as they maximize the signal-to-noise ratio (SNR)

Filters are indispensable in any RF/microwave system, as they maximize the signal-to-noise ratio (SNR). When filters are realized using passive devices smaller than the circuit operating wavelength, they form lumped element filters. Lumped element filter design involves the calculation of passive component values that satisfy design requirements. In this article, we will discuss lumped element filters and the use of the insertion loss method to design them.

Lumped Element Filters

Filters are two-port reciprocal networks made of passive elements that allow a frequency band to pass through them, and, at the same time, block signals outside the passband. Types of filters include RLC filters, active filters, cavity filters, and ceramic resonator filters. When filters are made of lumped elements, they are called lumped element filters.

Features of Lumped Element Filters

Lumped element filters are based on passive devices such as resistors, capacitors, and inductors. Usually, filter circuits are reciprocal, and the passive devices do not add energy to the input or output signals of the filter. 

The features of lumped element filters are such that none of them exceed 1/10 of a wavelength at the maximum frequency of operation. Compared to their distributed element counterparts, they possess advantages such as a lower cost, smaller footprint, and wider bandwidth. There is only a minimal phase shift between the input and output waveforms of lumped element filters.

Types of Lumped Element Filters 

Low Pass Filter

A low pass filter (LPF) is capable of modifying, reshaping, and rejecting all unwanted high frequencies from a signal and passing only the wanted signals in the desired frequency band. LPFs produce high signal attenuation above a specified frequency, called cut-off frequency or corner frequency. Below cut-off-frequency, they produce no attenuation. The simplest low pass lumped element filter consists of a resistor and capacitor, but the design complexity increases with functionalities and as more components, such as series inductors and parallel capacitors, are introduced to the filter circuit. 

High Pass Filter

A high pass filter (HFP) passes through signals higher than the cut-off frequency and attenuates all lower frequencies. The attenuation level varies with the filter design. The majority of applications of HPF are in radio frequency devices to remove the DC offset from the signals. HFPs can also be used along with LPFs to form a bandpass filter.

Bandpass Pass Filter 

When a lumped element filter passes through signals within a certain frequency band and discards signals outside the band, the filter is called a bandpass filter (BPF). An RLC circuit is an example of a BPF in analog electronics circuits.

Lumped Element Filter Design Using the Insertion Loss Method

The insertion loss method introduces network synthesis techniques to design filters of desired characteristics. The lumped element filter design procedure includes low-pass filter prototypes that are normalized in terms of impedance and frequency. Transformations are applied to the low-pass filter prototype to achieve the final filter design. 

The Procedure for the Insertion Loss Method

The procedure for the insertion loss method is as follows:

1. Define filter specifications: The cut-off frequency, stop-band attenuation, pass-band insertion loss, and pass-band behavior are defined for the filter. The final filter design should satisfy all these specifications.

2. Design a low-pass prototype circuit: In this prototype circuit, generally, designers choose the source impedance to be Rs=1 ohm and the cut-off frequency to be 𝜔c =1 rad/sec. Filter tables and computer packages are utilized for this step. In low pass prototyping, types of low pass filters (such as Butterworth or Chebyshev) are modeled to satisfy design requirements. 

3. Scale and convert: The filter should be scaled to the proper impedance level in this final stage. The design can be converted to a high-pass filter, band-pass filter, or band-stop filter. 

4. Implement: The designed filter is hardware-implemented using lumped elements. 

Lumped element filter design using insertion loss is simple, yet it adheres to design specifications perfectly. 

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