# Active Band Pass Filters Information

Active band pass filters (BPF) attenuate frequencies below and above a range of frequencies (i.e., the bandwidth or passband of the filter). Any signal with a frequency within that band pass range passes easily through the filter. Any frequency outside of the band pass is attenuated or reduced. There are two basic types of active band pass filters: switched capacitor and continuous. Switched capacitor active band pass filters are clocked devices. The input signal is sampled at a high rate and processed discretely instead of on a continuous-time basis. Continuous active band pass filters have a continuous time operation.

For in-depth background information on electronic filter design and theory, please visit the Electronic Filters Specification Guide.

## Theory

An active band pass filter can be built by cascading a high pass filter, an amplifier and a low pass filter, as shown in the block diagram below.

An example of a simple single-pole inverting band pass filter is shown below.

The first stage is a one-pole high pass filter in which the capacitor is directly connected to the source to block any DC voltage from the source. It is followed by an inverting amplifier, and the last stage is a low pass filter. The amplifier provides gain for the filter as well as isolation between the two stages.

The gain of the amplifier is given by

The critical frequencies are determined as follows:

Adding the frequency responses of these stages together results in the frequency response of the band-pass filter, as shown below.

The amplitude and phase are given by the following equations.

A Bode plot of a BPF with fL=100 Hz and fH=2 x 104 Hz is shown in the following figure:

### Bandwidth

The bandwidth of a BPF is defined as the range of frequencies of the filter's passband, or the frequencies form the low cut-off to the high-cut-off frequencies. In equation form:

The center frequency is defined as the highest frequency in the passband, representing the filter's resonant frequency. Because the BPF has at least two reactive components (capacitors), the filter will have a peak value at this frequency. The geometric mean of the two cut-off frequencies is given by

### Quality Factor

The quality factor or Q-point is a figure of merits that describes a filter's selectivity, and is a measure of the bandwidth's size. A filter with a small Q value has a large bandwidth, whereas a large Q indicates a BPF with a small bandwidth. In the latter case the filter may be referred to as "selective." As a standard, a filter with a Q value larger than 10 is said to be "highly selective." Th Q-factor is defined as follows:

The body diagram shown previously shows a filter with Q equal to

The Bode plot of this filter shows that its bandwidth is large. A typical BPF with a large Q (small BW) is depicted below.

### Inverting BPF Circuits

The circuit in the previous section always produces a low Q-point, or a large bandwidth. A BPF with a much bigger Q-point, or a very small bandwidth is produced by re-arranging the capacitors and resistors:

The transfer function of the above circuit is given by

And its amplitude frequency response is similar to the following figure.

Note the high selectivity of this filter due to its short bandwidth.

The two cut-off frequencies and the center are given by

And the gain is

A very highly selective filter, with a high Q-point (Q  <=  25) and very steep roll-off is produced by rearranging the capacitors and resistors in the previous circuit once more. There are two versions of this circuit, which is also called an infinite-gain multiple-feedback (IGMF) filter, as shown in the following figures.

Figure a: Multiple-feedback BPF with R3

Figure b: Multiple-feedback BPF without R3

## Filter Specifications

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

Cutoff or center frequency. The filter type determines the specified frequency (Fc). For band pass and band reject filters, the specified frequency is the center frequency.

Bandwidth. The bandwidth is the range of frequencies that filters pass with minimal attenuation or, in the case of band reject filters, maximum 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. Operating temperature is the value specified by a level of the ambient temperature (in °C) in which the filter was 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 filter. 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 filter. Butterworth filters are designed so that the frequency response is flat in the passband.
• Chebyshev filter. Chebyshev filters feature a very steep roll-off, but have ripples in the passband.
• Elliptic filter. Elliptic filters (Cauer filters) exhibit equalized ripple in both the passband and the stopband.
• Gaussian filter. Gaussian filters produce no overshoot in response to an input step. They optimize the rise and fall times.
• Legendre filter. 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. Dual in-line package (DIP) is a type of semiconductor component packaging. DIPs 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. There are several types of DIP packages, such as ceramic dual in-line package (CDIP), plastic dual in-line package (PDIP), and shrink plastic dual in-line package (SPDIP).
• CDIP. Ceramic dual in-line packages (CDIP) 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 (PDIP) 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. DPAK refers to a type of transistor outline package (TO-252).
• CSP. Chip scale package or chip size package (CSP) 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. SIP refers to a single inline package.
• SOIC. SOIC refers to a small outline IC.
• SSOP. SSOP refers to a shrink small outline package.
• SOP. SOP is a small outline package.
• MSOP. Mini small outline plastic package (MSOP) products are packed in tape reel assemblies that include a carrier tape with embossed cavities for storing individual components. The carrier tape is made from dissipative polystyrene resin. 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. SOT packaging refers to a small outline transistor.
• SOPT23. SOT23 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. PSOP refers to a power small outline package.
• QFP. QFP is a quad flat package.
• TO-220. Transistor outline (TO) is a standard package for discrete transistors. TO-220 is a TO package of size 220.
• TO-3. Transistor outline (TO) is a standard package for discrete transistors. TO-3 is a TO package of size 3.
• SC-70. 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.
• TSSOP. TSSOP refers to thin shrink small outline L-leaded packages.
• QSOP. QSOP refers to a quarter size outline package.
• PLCC. PLCC refers to a plastic leaded carrier.
• UCSP. UCSP refers to an ultra chip scale package.