Active filters for video meet antialiasing and reconstruction requirements

High-performance op amps and specialized software for PCs enable the design of wide-bandwidth active filters, but those advantages don't address the requirements of any specific application. For video filters, the application and signal format add nuance to each circuit design. The two major video applications are antialiasing filters and reconstruction filters.

Antialiasing filters, which precede an ADC, attenuate signals above the Nyquist frequency, or one-half the sample rating of the ADC. These filters usually have the steepest possible response to reject everything above the cutoff frequency. (The filter response drops by –3 dB at the cutoff frequency.) For ITU-601 applications and others, analog filters combined with digital filters and an oversampling ADC help to achieve this performance. Little filtering is necessary for applications such as PC graphics.

Reconstruction filters, also called (sinx)/x or zero-order-hold correctors, follow DACs to remove multiple images that the sampling creates but not to remove the DAC clock. Reconstruction filters are seldom as selective as antialiasing filters because the DAC's hold function also acts as a filter—an action that lowers the required selectivity but introduces loss in the response. The available video formats are RGB, component video, composite video, and RGB PC graphics.

All applications and formats require a video filter to be "phase linear," a condition that group delay (delay versus frequency) specifies. The degree of required phase linearity depends on the application and the video format. For example, antialiasing filters and component formats have tighter phase-linearity specifications than reconstruction applications and composite video. NTSC, PAL/DVB, ITU, SMPTE, and VESA specify the requirements for the various applications and formats.

You can compare filters to determine the optimum design for a given application or format. Some examples that follow compare Rauch and Sallen-Key realizations with regard to their gain-bandwidth-to-cutoff ratios, using predistortion and element-sensitivity techniques to achieve accuracy in the design. The examples include an ITU-601 antialiasing filter; a 20-MHz antialiasing and reconstruction filter; and an HDTV-reconstruction filter.

Whether you use a video filter for antialiasing or reconstruction, the filter must have a lowpass characteristic to pass the video-frame rate. You should therefore beware of ac coupling. The industry categorizes lowpass filters by their amplitude characteristic or by the name of the polynomial, such as Bessel, Butterworth, Chebyshev, or Cauer, that describes it. Figure 1 shows these characteristics normalized to a 1-rad bandwidth. Normally, you'd choose a filter with the best selectivity and the fewest poles to minimize cost, but the additional need for phase linearity limits the available choices.

A filter's phase linearity is specified as envelope delay or group delay versus frequency. A flat group delay indicates that all frequencies are delayed by the same amount, which preserves the shape of the waveform in the time domain. Thus, absolute group delay is less important than the variation in group delay. (Do not confuse group delay with channel-to-channel variation, which is specified as "time coincidence.")

Group delay is undesirable but not unacceptable for video, so you may ask how much is acceptable and why it is acceptable. The answer depends on the application and the video format. For example, ITU-470 loosely specifies group delay for composite video, but ITU-601 specifies it tightly to ensure "generational stability," both for MPEG-2 compression and to control phase jitter before serialization. So, you may need to know what filter characteristics to look for to ensure phase linearity.

The group-delay curves in Figure 1 show a peak near the cutoff frequency (ω/ω_C=1). The steep phase change near the cutoff frequency causes this problematic peak. To get an idea of scale, a three-pole, 6-MHz Butterworth filter has a group-delay variation of 20 to 25 nsec over its bandwidth. Adding poles or increasing the filter's selectivity increases that variation. Other, more exotic filters that minimize group-delay variation include Bessel, phase approximation, Thompson-Butterworth, and LeGendre (Reference 1). Nevertheless, the Butterworth characteristic is most common for video.

All formats and applications are sensitive to group-delay variation. The degree of sensitivity depends on the number of signals and their bandwidths. Composite NTSC/PAL has only one signal, and ITU-470 specifies group delay. Those requirements are easy to meet. RGB and component video both have multiple signals. The RGB signals have equal bandwidths, but component-video signals do not, making group-delay matching easy with RGB but difficult with component video.

Because the Pb and Pr signals have half the bandwidth of the luma (Y) signal, their group delay is double that of the Y signal. One approach is to slow the Y signal by adding delay stages. Another is to equalize bandwidths by doubling the sample rates of Pb and Pr. That approach raises the 4:2:2 sampling rate to 4:4:4, allowing you to treat the signal as RGB. (The 4:2:2 sampling originally indicated the number of times the color subcarrier was oversampled. ITU-601 replaced the subcarrier frequency with 3.375 MHz. The 4:2:2 sampling occurs at 13.5 and 6.75 MHz.) Reconstruction applications discard or average the additional Pb and Pr samples during antialiasing.

The other component-video format (S-VHS) is confusing to some. The Y channel is the same as in YPbPr, but the chroma signal, C, looks like it needs bandpass filtering rather than lowpass filtering. As for YPbPr signals, bandpass filtering causes group-delay and timing problems, so don't do it! Unless you're encoding analog signals, you can lowpass-filter Y and C with the same filter. S-VHS is more forgiving of bandwidth limitations than of problems caused by trying to equalize the delay. You typically see S-VHS in reconstruction applications, for which the main concern is correct timing between Y and C.

After choosing a filter characteristic, the next step is to implement it with an actual circuit. The most commonly used single-op-amp circuits are the Sallen-Key configuration in noninverting form and the Rauch configuration in inverting form. An important consideration for op amps operating in the wide bandwidths of video applications is the minimum gain bandwidth. Video signals are typically 2V p-p, so you need to refer to the large-signal gain bandwidth. Don't confuse that parameter with the 2V p-p, 0.1-dB gain bandwidth, which is much lower.

For filter circuits, an important question to answer is how much larger than the filter's cutoff frequency does the op-amp gain bandwidth have to be? For a Rauch filter, the phase argument of the filter's response characteristic is

ARG[K(j_ω)]NONINV=

–(ω_C/GBW_RAD)(1+R_F/R_I). (1)

For a Sallen-Key filter, the argument is

ARG[K(j_ω)]NONINV=π

–(ω_C/GBW_RAD)(1+R_F/R_I). (2)

In these equations, R_F and R_I are the gain-set resistors in ohms, GBW_RAD is the op amp's gain-bandwidth product, and ω_C is the filter's cutoff frequency in radians per second. You set the gain by introducing values for R_F and R_I and solving for ω_C/GBW_RAD. For the noninverting case, R_FR_I=0, and, for the inverting case, R_F/R_I=1. A unity-gain Rauch circuit has R_F/R_I=1, and a Sallen-Key circuit has R_F/R_I=0. Thus, for the same phase error, a Sallen-Key circuit requires half the gain bandwidth of a Rauch circuit. As the required gain increases, the phase error of the two circuit types converges, leaving little advantage for the Sallen-Key in gain bandwidth, but you must also consider other issues.

Anything less than an infinite GBW_RAD/ω_C ratio causes the closed-loop poles of a filter to move. For this reason, an actual filter often exhibits a lower bandwidth (ω_C) than does the paper design (Reference 2). You can compensate for this effect with predistortion by increasing the design bandwidth. Formulas for the Sallen-Key and Rauch circuits help to calculate a design bandwidth that provides the actual necessary bandwidth (Table 1 and Table 2).

The next design aspect to consider is component tolerance. To determine component tolerance, you need a sensitivity function (Reference 3): S_X^Y gives the ratio between a change in the value of part X and the consequent change in parameter Y. For example, Table 1 shows that the Q in a Sallen-Key circuit has greater sensitivity to variations in C₁ and C₂ than does Rauch circuit. Thus, a Sallen-Key filter is less tolerant of parasitics than a Rauch filter. The sensitivity function, S_X^Y, lets you predict the effect and then design accordingly. Now, consider some typical designs.

For antialiasing filters, a template such as the one in Figure 2 for ITU-601 determines the sensitivity. The specified bandwidth is 5.75 MHz±0.1 dB with an insertion loss of 12 dB at 6.75 MHz and 40 dB at 8 MHz and with a group-delay variation of ±3 nsec over the 0.1-dB bandwidth. Such performance is too difficult for an analog filter alone, but four-times oversampling modifies the requirements to 12 dB at 27 MHz and 40 dB at 32 MHz.

Using software or normalized curves, you find that a five-pole Butterworth filter with a –3-dB bandwidth of 8.45 MHz satisfies the requirement for selectivity but not for group delay (Reference 1). You need a delay stage, for which the important op-amp parameter is the 0.1-dB, 2V p-p bandwidth. You use this bandwidth number in equations 1 and 2 to get an accurate design. A schematic for this application with curves showing its gain and group-delay characteristics, uses four-times oversampling (Figure 3).

Next, consider PC video. VESA does not specify templates for antialiasing or reconstruction filters. The XGA resolution (1024×768 pixels at 85 Hz) has a sampling rate of 94.5 MHz and a Nyquist frequency of 47.25 MHz. A Rauch realization of a 20-MHz, four-pole Butterworth filter achieves greater than 35-dB attenuation at the Nyquist frequency (Figure 4). This design uses the MAX4450/4451 for its transient-response characteristic and signal bandwidth of 175 MHz at 2V p-p.

Many designers do not fully understand reconstruction filtering after a DAC. Designers often think that the purpose of reconstruction filters is to remove the sample clock, but nothing is further from the truth. When a system samples a signal, the samples comprise multiple recurring images of the signal centered on harmonics of the sample clock. A reconstruction filter removes all but the baseband sample. If the antialiasing filter has done its job, the DAC output looks like Point A in Figure 5, and you then want to remove all samples to the right of it. Thus, reconstruction is similar to antialiasing except, because each sample exists only for an instant, the DAC holds it for one clock period, thereby creating the familiar staircase approximation to a sloping line.

The hold function corresponds to a digital filter whose Sinc-function characteristic, or sinx/x, is similar to that of a Butterworth or a Bessel filter (Figure 6). Notice that the response is down 4 dB at half the sample frequency. The second job of a reconstruction filter is to restore that loss, which requires an amplitude equalizer (Figure 7a). This equalizer is based on a delay stage and has a response like a Bessel filter. The design of the equalizer is based on the DAC sample rate, F_S. Figure 7b shows the DAC's frequency response with and without an amplitude equalizer. Like the delay stage, you can include an equalizer in any reconstruction filter.

The hold response also has a pole centered on the sample clock, which completely removes the clock. Nevertheless, most reconstruction applications refer to clock attenuation as a figure of merit.

The most common requirement for NTSC/PAL reconstruction is an attenuation of greater than 20 dB at 13.5 MHz and greater than 40 dB at 27 MHZ, where ω_C depends on the applicable video standard. A three-pole Butterworth with Sallen-Key configuration is a good choice for two reasons. First, its gain of 2 drives a back-terminated cable. Second, you can adjust the group-delay variation to optimize performance without using a delay equalizer. Figure 8 shows both NTSC and PAL designs and the corresponding gain and group-delay characteristics. These applications usually include digital amplitude correction for the DAC, but you can easily add that feature if necessary.

To illustrate a circuit for XGA, a 20-MHz, three-pole Butterworth filter in the Sallen-Key configuration includes Figure 8's circuit for amplitude correction. (See Figure 9.) Complementing the antialiasing filter of Figure 4, this filter has a gain of 2 to drive a back-terminated, 75Ω coaxial cable.

The last application is a reconstruction filter for HDTV. Based on the templates in SMPTE 274 and 296M, it has a center frequency of ω_C=0.4×F_S=29.7 MHz. The DAC usually includes amplitude correction, but you need to add group-delay compensation. The resulting 30-MHz, five-pole Sallen-Key filter has greater than 40-dB attenuation at 74.25 MHz and a group-delay stage with gain of 2 to drive a back-terminated, 75Ω coaxial cable. (See Figure 10.)

Whether you design filters by hand, with the aid of software, or with a combination of these approaches, the actual response may differ from what you expect. One cause is the discrepancy between a calculated response and the actual response you obtain using standard component values.

You can minimize error by choosing standard 5% capacitor values and deriving the resistor values from them. The reason is practical: Capacitors are available with 1 or 2% tolerance but only at 5% values, whereas resistors are available that combine 1% values with 1% tolerance. Such components give the best approximation and the most precise amplitude response.

Once you build it, a filter may be unstable and oscillate. In that case, short the input to ground and see whether it continues to oscillate. If it stops, the impedance is too high. Lowering the design impedance should eliminate the oscillation. If it continues, note whether the oscillation is near or just below the filter cutoff frequency. If it is just below the cutoff frequency, the oscillation is probably due to components or parasitics. If the oscillation is above the cutoff frequency, it's probably due to the op amp or the circuit layout.

Good layout seems an art, but it's based on a few simple principles, such as having a clean supply voltage and a solid ground. At minimum, that requirement means filtering with low-ESR capacitors and sometimes with a regulator. The loop that the bypass-capacitor connections form must be small, or the resulting parasitic inductance will resonate with the capacitance. A good ground plane is essential to good analog design, but as bandwidth increases, the ground plane may add parasitic capacitance that can detune the filter. To avoid that problem, remove the ground plane beneath the offending parts and traces.