Doug Kerr
Well-known member
In a recent essay on antialising in digital imaging and in digital audio, I made reference to the fact that when digital transmission of audio signals was introduced into the telephone network for general use, the "payload" audio signal that was accommodated was considered to have an upper frequency limit of 3450 Hz. I mentioned that this was a "legacy" value coming from several vintages of analog transmission systems.
Although it has almost nothing to do with photography, still some people here might be curious as to what that means. so I'll tell the story, which is truly fascinating.
Wired telephone circuits
Especially when implemented with pairs in a cable (as contrasted with "open wire"), a passive wired telephone circuit is essentially a distributed R-C (resistance-capacitance) filter. The resistance is of course that of the conductors, and the capacitance is that between the conductors. Its attenuation has a certain base value at low frequencies, and rises smoothly with frequency. The loss of energy is of course from dissipation as the signal current flows through the resistance of the conductors themselves.
The contribution of Pupin
The mathematician Michael Pupin showed that if we would introduce discrete inductance in series with the circuit conductors at periodic intervals, the circuit would become a, multi-section R-L-C (Resistance-inductance-capacitance) filter - in fact, it would approximate an L-C filter. This filter has a fairly constant attenuation over a substantial range of frequencies, and then the attenuation rises rather swiftly with further increase in frequency.
But in the region "below cutoff", the attenuation is significantly lower than it would be for the basic circuit at those same frequencies!
This at first seems counter-intuitive. But there is a simple explanation. The "multi-section filter", still considered a transmission line, has a significantly higher characteristic impedance than the "plain" circuit. Thus,assuming it is operated at its characteristic impedance, for a certain energy in the signal, the voltage is higher and the current less. Since the loss of energy follows, in fact, the square of the current, the attenuation is less. What a deal?
In the US, this came to be know as "inductive loading", loading coming from this metaphor. We have a stretched rope, down which we send a wave by moving the end up and down. If the were to crimp little weights along the rope at periodic intervals ("load it"), its properties would be like those of the transmission line with added inductance. In Europe, it came to be generally known as "Pupinization" in honor of the developer.
Standard inductive loading plans
Now, to actually exploit this, standardized plans had to be devised. One issue was of course the range of frequencies to be accommodated. I'm not familiar with the rationale for this, but for general use, it was decided to accommodate signals with a maximum frequency of 3450 Hz. This resulted in certain standard plans the the introduction of discrete inductors ("loading coils" in the US, "Pupin coils" in Europe). The most common such plan, based on cable whose pairs had a certain capacitance per foot (uniform even over different conductor gauges) introduced 88 mH of equivalent total series inductance every 6000 feet.
The power of legacy
Now, the value 3450 Hz as the upper frequency limit of our "general purpose payload" influenced several generations of transmission systems, ultimately the first digital transmission system, the T1 Carrier system. This led to the use there of a sampling frequency of 8000 Hz, with a resulting Nyquist frequency of 4000 Hz, so that signals with frequencies up to 3450 Hz could be properly handled and the design of the needed antialising filter would be economical.
To carry forward the story of the power of legacy, an important early issue in the design of the T1 Carrier was how far apart would the repeaters (devices that regenerated and revitalized the digital pulses, which of course would be attenuated by passage through the bearing cable pairs) be placed.
Well, in converting a cable from operation with inductively loaded passive pairs to digital operation, the loading coils had to be removed (as the bandwidth of the train of digital pulses was far greater than 3450 Hz - the pulse rate was eventually set at 1.544 MhZ). Of course, the attenuation would be high, but the digital mode of operation could tolerate that.
Thus, if the spacing of the repeaters were made 6000 feet, then a crew could set up a work site where the loading coils were, remove them from the pairs, and splice in a stub leading to a digital repeater cabinet placed just below. Minimum fuss, minimum muss!
Thus the repeater spacing for the T1 Carrier system was made 6000 feet, and the rest of the system design unfolded from that.
Best regards,
Doug
Although it has almost nothing to do with photography, still some people here might be curious as to what that means. so I'll tell the story, which is truly fascinating.
Wired telephone circuits
Especially when implemented with pairs in a cable (as contrasted with "open wire"), a passive wired telephone circuit is essentially a distributed R-C (resistance-capacitance) filter. The resistance is of course that of the conductors, and the capacitance is that between the conductors. Its attenuation has a certain base value at low frequencies, and rises smoothly with frequency. The loss of energy is of course from dissipation as the signal current flows through the resistance of the conductors themselves.
The contribution of Pupin
The mathematician Michael Pupin showed that if we would introduce discrete inductance in series with the circuit conductors at periodic intervals, the circuit would become a, multi-section R-L-C (Resistance-inductance-capacitance) filter - in fact, it would approximate an L-C filter. This filter has a fairly constant attenuation over a substantial range of frequencies, and then the attenuation rises rather swiftly with further increase in frequency.
But in the region "below cutoff", the attenuation is significantly lower than it would be for the basic circuit at those same frequencies!
This at first seems counter-intuitive. But there is a simple explanation. The "multi-section filter", still considered a transmission line, has a significantly higher characteristic impedance than the "plain" circuit. Thus,assuming it is operated at its characteristic impedance, for a certain energy in the signal, the voltage is higher and the current less. Since the loss of energy follows, in fact, the square of the current, the attenuation is less. What a deal?
In the US, this came to be know as "inductive loading", loading coming from this metaphor. We have a stretched rope, down which we send a wave by moving the end up and down. If the were to crimp little weights along the rope at periodic intervals ("load it"), its properties would be like those of the transmission line with added inductance. In Europe, it came to be generally known as "Pupinization" in honor of the developer.
Standard inductive loading plans
Now, to actually exploit this, standardized plans had to be devised. One issue was of course the range of frequencies to be accommodated. I'm not familiar with the rationale for this, but for general use, it was decided to accommodate signals with a maximum frequency of 3450 Hz. This resulted in certain standard plans the the introduction of discrete inductors ("loading coils" in the US, "Pupin coils" in Europe). The most common such plan, based on cable whose pairs had a certain capacitance per foot (uniform even over different conductor gauges) introduced 88 mH of equivalent total series inductance every 6000 feet.
The power of legacy
Now, the value 3450 Hz as the upper frequency limit of our "general purpose payload" influenced several generations of transmission systems, ultimately the first digital transmission system, the T1 Carrier system. This led to the use there of a sampling frequency of 8000 Hz, with a resulting Nyquist frequency of 4000 Hz, so that signals with frequencies up to 3450 Hz could be properly handled and the design of the needed antialising filter would be economical.
To carry forward the story of the power of legacy, an important early issue in the design of the T1 Carrier was how far apart would the repeaters (devices that regenerated and revitalized the digital pulses, which of course would be attenuated by passage through the bearing cable pairs) be placed.
Well, in converting a cable from operation with inductively loaded passive pairs to digital operation, the loading coils had to be removed (as the bandwidth of the train of digital pulses was far greater than 3450 Hz - the pulse rate was eventually set at 1.544 MhZ). Of course, the attenuation would be high, but the digital mode of operation could tolerate that.
Thus, if the spacing of the repeaters were made 6000 feet, then a crew could set up a work site where the loading coils were, remove them from the pairs, and splice in a stub leading to a digital repeater cabinet placed just below. Minimum fuss, minimum muss!
Thus the repeater spacing for the T1 Carrier system was made 6000 feet, and the rest of the system design unfolded from that.
Best regards,
Doug