AN-945 APPLICATION NOTE

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Tyrone Boyd
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1 APPLICATION NOTE One Technology Way P.O. Box 96 Norwood, MA , U.S.A. Tel: Fax: System Bandwidth vs. Resolution or Analog Video by Ferenc Barany INTRODUCTION Ensuring the best quality picture is the ultimate goal or video system designers. With the introduction o HDTV, image resolution as well as video signal bandwidth has increased dramatically. Because video systems tend to support multiple resolutions and interaces, design engineers must careully examine the system bandwidth requirements to ensure that signals are not distorted. This application note provides a quick overview o the videospeciic terms used to characterize system bandwidth and how they relate to 3 db bandwidth. SYSTEM BANDWIDTH DEFINITIONS Generally, 3 db bandwidth is a measure o a system s bandwidth. Assuming a low-pass requency response, 3 db bandwidth is deined as the requency at which the output power drops to hal o the output power at dc. This translates into a 29.3% drop in the output voltage compared with dc. For video applications, 3 db bandwidth has little meaning because it doesn t directly relect the attenuation o the video signal components. The video literature mentions the term gain latness, which represents the maximum allowable drop in signal amplitude within the pass band. Tests have revealed that the human eye is unable to distinguish brightness variations o less than 1%, which translates into a.1 db signal drop within the pass band, or put simply,.1 db gain latness. A more liberal approach allows about 6% signal drop, which translates into.5 db gain latness. The ollowing sections describe the relationship between the.1 db and.5 db gain latness speciications and 3 db bandwidth. The examples assume a Butterworth requency response, which is the most common response. 75Ω V IN H(s) V OUT 75Ω H(s) = VIDEO SYSTEM FREQUENCY RESPONSE V IN = VIDEO INPUT SIGNAL V OUT = VIDEO OUTPUT SIGNAL Figure 1. Video System Frequency Response Rev. Page 1 o 8

2 TABLE OF CONTENTS Introduction... 1 System Bandwidth Deinitions... 1 Low-Pass Frequency Response... 3 High-Pass Frequency Response...4 Conclusion...4 Rev. Page 2 o 8

3 LOW-PASS FREQUENCY RESPONSE The transer unction o a low-pass Butterworth response HLP(), is given by the ollowing ormula: H where: LP ( ) = 1+ 1 C C is the cuto requency. is the signal requency. n is the order o the system. Figure 2 illustrates the low-pass Butterworth response with C = 1 MHz or to dB ATTENUATION POINT Figure 2. Low-Pass Butterworth Frequency Response The attenuation o the low-pass ilter can be calculated using the ollowing ormula: (1) AN-945 I AdB is.1 db or.5 db, depending on the two video gain latness speciications, the ratio between the cuto requency and the maximum video requency or various system orders is listed in Table 1. Table 1. Low-Pass C or.5 db and.1 db Gain Flatness Gain Flatness C /MAX Ratio.1 db db Figure 3 and Figure 4 illustrate the low-pass requency responses or 1 MHz.5 db and.1 db gain latness speciications. In addition, the attenuation axis is intentionally limited to 3 db to highlight the 3 db bandwidth as the intersection o each plot with the requency axis dB GAIN FLATNESS POINT Figure 3.Low-Pass Cuto Frequencies or Normalized Systems (.5 db Flatness) A db = log 1 + (2) C.5 By substituting with the maximum video requency (MAX), the ratio between the cuto requency, C, and the maximum video requency, MAX, can be expressed as C MAX 1 = (3) AdB dB GAIN FLATNESS POINT Figure 4. Low-Pass Cuto Frequencies or Normalized Systems (.1 db Flatness) Rev. Page 3 o 8

4 HIGH-PASS FREQUENCY RESPONSE When ac coupling is used, the high-pass ilter ormed by the ac coupling capacitor and the input impedance o the video receiver attenuates low requency signals. The Butterworth high-pass transer unction, HHP(), is given by the ollowing ormula: H HP 5 ( ) = 1 C 1 + Figure 5 illustrates the high-pass Butterworth response or a system with C = 1 MHz and to 5. (4) Figure 5 and Figure 6 illustrate the high-pass requency responses or 1 MHz.5 db and.1 db gain latness speciications. In addition, the attenuation axis is intentionally limited to 3 db to highlight the 3 db bandwidth as the intersection o each plot with the requency axis dB GAIN FLATNESS POINT 5 3dB ATTENUATION POINT Figure 6. High-Pass Cuto Frequencies or Normalized Systems (.5 db Flatness) Figure 5. High-Pass Butterworth Frequency Response The attenuation o the high-pass response is given by C A db = log 1 + (5) Substituting with the minimum video requency (MIN), the ratio between the cuto requency, C, and the minimum video requency, MIN, can be expressed as C MIN AdB 1 = (6) The ratio between the cuto requency and the minimum video requency corresponding to.1 db and.5 db gain latness respectively is listed in Table 2 or various system orders. Table 2. High-Pass C or.5 db and.1 db latness Gain Flatness C /MIN Ratio.1 db db dB GAIN FLATNESS POINT Figure 7. High-pass Cuto Frequencies or Normalized Systems (.1 db Flatness) CONCLUSION When designing video systems, the design engineer must careully analyze the required system bandwidth to ensure optimum perormance. Once the gain latness speciication is set, the engineer can derive the required 3 db bandwidth or the system based on the requency response type and order o the system. Table 3 and Table 4 contain the 3 db bandwidth required (cuto requencies) or various video resolutions including TV and PC graphics standards, or both the dc- and accoupling options. The Butterworth requency response is assumed, and to Rev. Page 4 o 8

5 Table 3. 3 db Bandwidth or DC-Coupled Systems (Low-Pass Response) Standard Aspect Ratio Reresh Rate (Hz) MAX (MHz) Low-Pass Cuto Frequency (C) in MHz.1 db Gain Flatness.5 db Gain Flatness 48i 4: : p 4: i 4: : p 4: p 16: i 16: : p 16: : VGA 4: : : : SVGA 4: : : : : XGA 4: : : : SXGA 5: : : UXGA 4: : : : : Rev. Page 5 o 8

6 Table 4. 3 db Bandwidth or AC-Coupled Systems (High-Pass Response) Standard Aspect Ratio Reresh Rate (Hz) MIN (Hz) Low-Pass Cuto Frequency (C) in MHz.1 db Gain Flatness.5 db Gain Flatness 48i 4: : p 4: i 4: : p 4: p 16: i 16: : p 16: : VGA 4: : : : SVGA 4: : : : : XGA 4: : : : SXGA 5: : : UXGA 4: : : : : Rev. Page 6 o 8

7 NOTES Rev. Page 7 o 8

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