HP Clock Wednesday, July 13, 2011

Why do we have 29.97 frame rates, and not just 30??

I get this question quite often, so I thought I would provide the best answer I could including some historical perspective.

The short answer is that it is due to making a less expensive and more reliable sound recovery circuit in black and white televisions in the 50s.
Here’s why.  Radios typically recover information by the nonlinear mixing of the radio frequency energy from the transmitter with that of a local oscillator.  The combination of the two signals will produce sum and difference frequencies, also known as high side and low side conversion.  The output of that mixer is applied to an IF amplifier that has a tuned bandpass for a single frequency. (IF = Intermediate Frequency).  Tuning in the radio is accomplished by changing the frequency of the local oscillator such that the combination of local oscillator plus the transmitting station or local oscillator minus the transmitting station matches the tuned response of the IF amplifier.  That way depending on the frequency of the local oscillator, only a single frequency or station can pass though the key-hole that is the IF filter and amplifier.
As specified in the early 40s, the NTSC originally had a frame rate of 30 and a line rate of 15,750.  Also early in the specification of television it was decided that the picture would be amplitude modulated on one carrier and the sound would be frequency modulated on a second higher frequency carrier separated enough to prevent the two signals from interfering with each other.  What this means is that a television essentially needed two radio receivers comprised of two mixers, two local oscillators, two IF amplifiers, and two detectors. One set of circuits for picture, and one set for sound.  The difficulty in this scheme is getting the two local oscillators to change frequency exactly the right amount every time the user changed channels.  This is further exacerbated by the inherent lack of stability of oscillators at these high frequencies.  There were no inexpensive phased lock loops and digital synthesizers in the 50s.  To eliminate the difficulty and expense of building two oscillators that would track each other and not drift apart it was decided that the tolerance of frequency separation could be held more precisely at a single location, the TV transmitter.  It was further decided to separate the visual and audio signals by exactly 4.5 MHz.  This allowed set manufacturers to design TV sets with inter-carrier sound detection, or a carrier within a carrier.  The system worked by using a single local oscillator, mixer and IF amplifier to detect the entire audio/video signal.  This means that the ‘baseband video’ at the output of the detector contained the audio at 4.5 MHz as well as the picture.  The detected signal was split with one side going to a 4.5 MHz tuned circuit called the ‘sound trap’ to remove the sound carrier from the picture. The other side went directly to a 4.5 MHz IF amplifier where it could be amplified to a usable level, no secondary local oscillator needed.  The output of this second IF amplifier could now be fed to an FM discriminator to extract the audio.
With the advent of color a third carrier needed to be added to the scheme.  This third carrier literally needed to be shoe-horned in between the visual signal and the audio signal.  If the frequency of the color carrier were to high it would interfere with the 4.5 MHz sound carrier.  If the frequency of the color carrier were to low artifacts would be seen in the picture.  Add to this that the color information added to the video signal could not obsolete the installed base of black and white televisions.  The decision was made to place the color carrier below the sound carrier and inband of the picture carrier.  This is illustrated in figure 1 below.

Fig. 1 Relationship between the luminance signal, sound signal and the color subcarrier.
• fs = Frequency of sound carrier
• fc = Frequency of chrominance or color carrier
• fh = Frequency of horizontal line rate

Since the frequency of the sound carrier could not change without making the legacy black and white TVs obsolete 4.5 MHz was made to be the 286th harmonic of the horizontal line rate.
286 = fs /fh
Using this equation the horizontal rate will be equal to the sound carrier divided by 286.  286 is the closest even number harmonic that will provide a ratio close to the original line rate of 15,750 KHz.
fh = fs/286
The color sub carrier frequency will need to be in the range of approximately 3.6 Mhz and an odd harmonic of the half horizontal line rate.  An odd harmonic that is half of the line frequency is desirable because the color subcarrier is ‘inband’ of the luminance signal, and because an odd harmonic half line rate will have opposite voltage polarities for the picture information on odd and even lines.  This method of reducing the interference of the color and luminance signal is known as frequency interlace.  The odd harmonic of the half line frequency closest to the original line rate of 15, 750 KHz would be 457/2.  However 457 is a prime number, making it difficult to derive other frequencies such as the horizontal and vertical rate.  The next best choice and the harmonic that was ultimately chosen was 455/2.  455 has the prime factors of 5, 7 and 13 making it easier to create frequency divider chains.
fc = (455/2)* fh
Again, the equation can be solved for the horizontal rate, but this time as it relates to the color carrier, and the selected harmonic of that carrier.
fh = 2*fc /455
Setting the two equations for the horizontal frequency equal to each other, one in terms of the sound carrier and the other in terms of the color carrier, the yet unknown horizontal rate drops out. Now the color carrier can be solved for and calculated exclusively in terms of the selected harmonics and the implacable 4.5 MHz sound carrier.
2*fc /455 = fs/286 = 4.5 MHz/286
fc = (455*4.5 MHz)/(2*286) = 3,579,545.4546 Hz
The Horizontal line rate can now be calculated based on the calculated color rate.
fh = 2*fc /455 = 15,734.2657 Hz
Dividing this new line rate into the original line rate gives the ratio of frequency reduction from the original black and white system to the NTSC color standard.
15,750 Hz/15,734.2657 Hz = 1.001
Ratio of Frequency Change = 1.001 : 1
Dividing the 1.001 frequency reduction coefficient into the original black and white 30 frames per second gives the color frame rate we are now familiar with.
30 fps/1.001 = 29.97
Bibliography
Donald G. Fink, Editor, Television Standards and Practice – NTSC, First Edition, New York, McGraw-Hill Book Company., 1943. (Appendix I)

Donald G. Fink, Editor, Television Engineering Handbook, First Edition, New York, McGraw-Hill Book Company., 1957. (Pg. 7-3 to Pg. 7-4, sec 7.103 Timing Relationships)

Bernard Grob, Basic Television, Principles and Servicing, New York, McGraw-Hill Book Company., 1964. (Pg. 523-524, sec 22.16 Intercarrier sound), (Pg. 580-582, sec 24.15 Color subcarrier frequency)

Howard W. Sams & Co., Reference Data For Radio Engineers, Sixth Edition, New York, McGraw-Hill Book Company., 1977.  (Pg. 30-31 Transmission Standards)