# Active Low Pass Filters Information

Low pass filters (LPF) pass signals from low frequencies and reject signals from high frequencies. Like other types of active filters, they use active components to shape and stabilize the behavior of the filter, and to serve as a buffer interface for the driven component. There are two basic classes of active low-pass filters: switched capacitor and continuous. Each type of device is available with first, second, third, fourth, fifth, sixth, seventh or eighth filter order. Switched capacitor filters are clocked devices. The input signal is sampled at a high rate and processed discretely instead of on a continuous-time basis. Continuous low-pass filters have a continuous time operation.

For in-depth details about electronic filter types and design, visit the Electronic Filter Specification Guide

## First-order Filters

The simplest one-pole LPF for low frequency applications can be constructed by connecting a resistor and a capacitor as shown below.

The equation of the gain, or transfer function is

Replacing the Laplace constant with its equivalent in terms of frequency yields

The magnitude or voltage gain is the absolute value of the transfer function, or

The critical frequency is defined as the frequency when the resistance (R) is equal to the impedance (reactance) of the the capacitor:

Therefore,

Substituting into this equation yields

The phase shift of the filter is given by

Or

A Bode plot (magnitude and phase as function of frequency) is shown in the following figure for

To calculate the cut-off and phase-shift of this filter:

and

If RC stages are cascaded together, the resulting network is an nth-order low-pass filter (n-pole filter). Such a network produces a roll-off of -20 dB/decade.

## Second-order Filters

A resistor and a capacitor can be used to create a simple first-order RC low pass filter as discussed above. This arrangement produces a roll-off slope of -20 dB/decade above the frequency of the cutoff or critical point at fc = 3 dB.

However, this roll-off may not be enough to remove unwanted signals. Using two filtering stages creates a steeper roll-off. Chaining two RC circuits (as shown in the figure below) produces a slope twice as large as a single stage. This figure shows a circuit that uses two passive first-order low-pass filters connected in series ("cascade") together to form a second-order (two-pole) filter network.

The following figure shows the Bode plots of one and two stages low-pass filters. The filter with the steepest roll-off is the second-order filter.

## Specifications

When selecting a low pass filter, the most important parameters include:

Cutoff or center frequency. The filter type determines the specified frequency (Fc).

Bandwidth. The bandwidth is the range of frequencies that filters pass with minimal attenuation.

Power dissipation. Power dissipation is the total power consumption of the device. Generally, this value is expressed in watts or milliwatts.

Supply voltage. Supply voltage (VS) refers to the source voltage range.

Supply current. Source current (IS or ICC) is the current produced by the supply source when connected to the amplifier.

Operating temperature. The ambient temperature range (in °C) within which the filter is designed to operate.

Number of poles. This is the order of the filter.

Pin count. Pin count is the number of physical connection points (e.g., pins, pads, balls) on the package.

### Filter Characteristics

• Bessel filters are active filters with a passband that maximizes the group delay at zero frequency, thus showing a constant group delay in the passband. Group delay is a measurement of the time it takes for a signal to move between two points in a network. A constant group delay in a filter's passband implies that for all signals with frequencies in the passband, the time delay will be the same. This fact is especially important in audio, video, and radar applications.
• Butterworth filters are designed so that the frequency response is flat in the passband.
• Chebyshev filters feature a very steep roll-off but have ripples in the passband.
• Elliptic filters (or Cauer filters) exhibit equalized ripple in both the passband and the stopband.
• Gaussian filters produce no overshoot in response to an input step and optimize rise and fall times.
• Legendre filters are designed to produce the maximum roll-off rate for a given order and a flat frequency response in the passband.

### Package Type

• DIP packages are installed in sockets or permanently soldered into holes extending into the surface of the printed circuit board. The pins are distributed into two parallel lines along opposite sides of the rectangular package.
• CDIP (ceramic dual in-line) packages consist of two pieces of dry pressed ceramic surrounding a "DIP formed" lead frame. The ceramic system is held together hermetically by frit glass reflowed at temperatures between 400-460° C.
• PDIP (plastic dual in-line package) is widely used for low cost, hand-insertion applications including consumer products, automotive devices, logic, memory ICs, micro-controllers, logic and power ICs, video controllers, commercial electronics, and telecommunications.
• DPAK refers to a type of transistor outline package (TO-252).
• CSP (chip scale package or chip size package) has an area that is no more than 20% larger than the built-in die. CSP is compact for second level packaging efficiency and encapsulated for second level reliability. CSP is superior to both direct-chip-attach (DCA) and chip-on-board (COB) technologies. CSP is used in a variety of integrated circuits (IC), including radio frequency ICs (RFIC), memory ICs, and communication ICs.
• SIP refers to a single inline package.
• SOIC refers to a small outline IC.
• SSOP refers to a shrink small outline package.
• SOP is a small outline package.
• MSOP (mini small outline plastic packages) are packed in tape reel assemblies that include a dissipative polystyrene resin carrier tape with embossed cavities for storing individual components. The cover tape is a multilayer film composed of a polyester film, adhesive layer, heat-activated sealant, and anti-static sprayed agent. The reel is made of polystyrene plastic (anti-static coated or intrinsic) and individually bar-coded. Reels are placed inside barcode-labeled boxes for shipping.
• SOT refers to a small outline transistor.
• SOPT23 is a rectangular, surface mounted, small outline transistor (SOT) package with three or more gull wing leads. SOT23 features a very small footprint and is optimized for the highest possible current. Because of its low cost and low profile, SOT23 is used in home appliances, office and industrial equipment, personal computers, printers, and communication equipment.
• PSOP refers to a power small outline package.
• QFP is a quad flat package.
• TO-220 is a standard  transistor outline (TO) package of size 220.
• TO-3 is a standard  transistor outline (TO) package of size 3.
• SC-70 is one of the smallest available IC packages. It is used in cellular phones, PDAs, electronic games, laptops, and other portable and hand-held applications where space is extremely limited.
• Other package types include thin shrink small outline (TSSOP), quarter-size outline (QSOP), plastic-leaded carrier (PLCC), and ultra-chip scale (UCSP).

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