Dual Compound
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Dual Compound
Dual-modulus prescaler
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The Dual modulus prescaler is an electronic circuit used in high-frequency synthesizer designs to overcome the problem of generating narrowly-spaced frequencies that are nevertheless too high to be passed directly through the feedback loop of the system.
The modulus of a prescaler is its division ratio. Dual-modulus means that it can divide by two different factors, usually M and M+1. Which factor is applied is changed using a control input. By careful arrangement, the system automatically operates to solve the problem at hand.
The Problem
A frequency synthesizer produces an output frequency f, which is the reference frequency fr x the division ratio N such that
f = Nfr
Since N is an integer, the output frequency must therefore be restricted to whole multiples of fr. Typically, these will be the channels for which the radio equipment is designed for, so fr will usually be equal to the channel spacing. For example, on narrow-band radiotelephones, a channel spacing of 12.5 kHz is typical.
Suppose that the divider N is only able to operate at a maximum clock frequency of 10 MHz, but the output f is in the hundreds of MHz range. If we interpose a fixed prescaler with a value M of say, 40, we can drop the output frequency easily into the operating range of the divider N. However, we have now introduced a factor of 40 into the equation, so the output frequency is now:
f = 40Nfr
If fr remains at 12.5 kHz, we can only obtain every 40th channel, not very useful. Alternatively if we reduce fr by a factor of 40 to compensate, the comparison frequency becomes 312.5 Hz, which is much too low to give good filtering and lock performance characteristics. It also means that programming the divider becomes more complex, as we need to only use those ratios that give us true channels, not the 1/40th of a channel that are now available!
The solution
The solution is the dual modulus prescaler. The main divider is split into two parts, the main part N and an additional divider A which is much shorter than N. Both dividers are clocked from the output of the dual-modulus prescaler, but only the output of the N divider is fed back to the comparator. Initially, the prescaler is set to divide by M+1. Both N and A count down until A reaches zero, at which point the prescaler is switched to a division ratio of M. At this point, the divider N has completed A counts. Counting continues until N reaches zero, which is an additional N-A counts. At this point the cycle repeats.
Thus:
f = fr((M(N-A) + A(M+1)))/N which reduces to f = fr((MN+A))/N
So while we still have a factor of M being multiplied by N, we can ADD an additional factor A, which effectively gives us a divider with a fractional part. Only the prescaler needs to be constructed from high-speed parts, and the reference frequency can remain equal to the desired output frequency spacing.
The diagram below shows the elements and arrangement of a frequency synthesizer with dual-modulus prescaler. (Compare with diagram on main synthesizer page).
One can compute A and N from the formula:
A = V mod M
N = V div M
where V is the combined division ratio (V = MN+A). For this to work properly, A must be strictly less than M, as well as less than or equal to N. These restrictions on values of A imply that you can't get every division ratio V. If V falls below M(M-1), some channels will be missing.
Specific Application Example
Dual modulus prescaler waveform with a 10 microsecond scale.
Dual modulus prescaler waveform with a 20 nanosecond scale.
Today, most dual-modulus prescalers exist inside of PLL chips, making it impossible to probe actual signals during operation. The first dual-modulus prescalers were discrete ECL devices, separate from the PLL chips. Here is an example of a dual-modulus prescaler in use. This circuit happens to use a Motorola MC145158 with a Fujitsu MB-501 dual-modulus prescaler operating in the 128/129 mode. The PLL is locked at 917.94 MHz [f in the equation] with a channel spacing frequency of 30 kHz [fr in the equation]. The total integer count therefore is 30598. Dividing this by 128 [M in the equation] yields a quotient of 239 with a remainder of 6, N and A respectively. The result of this frequency choice is that the prescaler spends most of its time counting at 128, and just a brief period at 129.
This is shown by the upper purple trace, the modulus control or counter output. These two screen captures differ only in the horizontal scale. The lower, yellow trace is the N counter output whose frequency corresponds to the channel spacing frequency of 30 kHz. The green trace is the output from the dual-modulus prescaler, which happens to correspond to 7.1714 MHz in the case...(and so on) To get More information , you can visit some products about Portable Pocket Radio, Digital Voice Recorder, . The Mechwarrior 4: Vengeance & Black Knight Software products should be show more here!
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can u simplify this? discrete math?
i have an expression p / (q V (r/T) and i have to Find the dual of the compound propositions. so i got ~p V (~q / (~ r V F))
I was wondering if (~ r V F) can simplified?
Yes.
A disjunction A V B is true when either A or B (or both) is true. In the disjunction (~ r V F), the right side is always false, so the expression is true exactly when ~r is true and is false exactly when ~r is false. Consequently:
(~ r V F) = ~r
Notice that the corresponding expression in the original proposition can also be simplified, because a conjunction is true exactly when both sides are true; since the right side of r/T is always true, the conjunction is true whenever r is true and false whenever r is false. Consequently:
(r / T) = r
A Dual Compound Tube Labelling system