Frequency of the j-k flip flop output signal formula
Answers
Explanation:
In the Sequential Logic tutorials we saw how D-type Flip-Flop´s work and how they can be connected together to form a Data Latch.
Another useful feature of the D-type Flip-Flop is as a binary divider, for Frequency Division or as a “divide-by-2” counter. Here the inverted output terminal Q (NOT-Q) is connected directly back to the Data input terminal D giving the device “feedback” as shown below.
Divide-by-2 Counter
frequency divider
It can be seen from the frequency waveforms above, that by “feeding back” the output from Q to the input terminal D, the output pulses at Q have a frequency that are exactly one half ( ƒ ÷ 2 ) that of the input clock frequency. In other words the circuit produces Frequency Division as it now divides the input frequency by a factor of two (an octave).
This then produces a type of counter called a “ripple counter” and in ripple counters, the clock pulse triggers the first flip-flop whose output triggers the second flip-flop, which in turn triggers the third flip-flop and so on through the chain producing a rippling effect (hence their name) of the timing signal as it passes through the chain.
The Toggle Flip-Flop
Another type of digital device that can be used for frequency division is the T-type or Toggle flip-flop. With a slight modification to a standard JK flip-flop, we can construct a new type of flip-flop called a Toggle flip-flop.
Toggle flip flops can be made from D-type flip-flops as shown above, or from standard JK flip-flops such as the 74LS73. The result is a device with only two inputs, the “Toggle” input itself and the negative controlling “Clock” input as shown.
74LS73 Toggle Flip Flop
toggle flip flop
A “Toggle flip-flop” gets its name from the fact that the flip-flop has the ability to toggle or switch between its two different states, the “toggle state” and the “memory state”. Since there are only two states, a T-type flip-flop is ideal for use in frequency division and binary counter design.
Binary ripple counters can be built using “Toggle” or “T-type flip-flops” by connecting the output of one to the clock input of the next. Toggle flip-flops are ideal for building ripple counters as it toggles from one state to the next, (HIGH to LOW or LOW to HIGH) at every clock cycle so simple frequency divider and ripple counter circuits can easily be constructed using standard T-type flip-flop circuits.
If we connect together in series, two T-type flip-flops the initial input frequency will be “divided-by-two” by the first flip-flop ( ƒ ÷ 2 ) and then “divided-by-two” again by the second flip-flop ( ƒ ÷ 2 ) ÷ 2, giving an output frequency which has effectively been divided four times, then its output frequency becomes one quarter value (25%) of the original clock frequency, ( ƒ ÷ 4 ).
Answer: Output is at half the frequency of the first. The output of the fourth cell is 1/16 the clock frequency.
Explanation:
The J and K inputs of each flip-flop are set to 1 to produce a toggle at each cycle of the clock input. For each two toggles of the first cell, a toggle is produced in the second cell, so its output is at half the frequency of the first. The output of the fourth cell is 1/16 the clock frequency. J-K flip-flops can be used to create a binary counter by connecting the output of one cell to the clock input of the following one. Each flip-flop has its J and K inputs set to 1, which results in a toggle for each cycle of the clock input. A toggle is created in the second cell for every two toggles of the first cell, and so on through the fourth cell. As a result, a binary number is generated that is equal to the input clock signal's cycle count. This tool is occasionally referred to as a "ripple through" counter. The same thing serves as an effective frequency divider.
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