# How to know the duty-cycle of a counter

Tags:
1. Jan 11, 2017

### Granger

1. The problem statement, all variables and given/known data
Consider the following circuit of a counter with a clock signal of 84 kHz

As we can see the counter counts down. Show all the states and transitions of this counter and identify all the states using a binary representation. Calculate the frequency and the duty-cycle of the signal labeled 2

2. Relevant equations
3. The attempt at a solution

So I didn't have any trouble with the first part of the problem, The states should be 1100 - 1011 - 1010 - 1001 - 1000 - 0111 and it repeats (so a total of 6 transitions).
Now the second part is the one that I'm not sure if I'm thinking correctly because this question never appeared to me.

My attempt to calculate the frequency. If I have 6 transitions all I have to do is to divide the clock frequency by the number of transitions (because If I had the period I would multiply it by the number of transitions). Anyway, I did it and obtained 14 kHz. Now the duty-cycle... I know what a duty-cycle. It's the percentage in the clock transition where the signal is high right? So it should be 1/6 = 17%....

I have no idea if I'm doing this correctly... I have a good feeling about the frequency but have no idea about the duty-cycle. Can someone give me some help? Thanks!

EDIT: The sequence is now correct

Last edited: Jan 11, 2017
2. Jan 11, 2017

### CWatters

Perhaps I'm a bit rusty but I'm struggling to understand this bit..

Shouldn't the sequence go..
1100
1011
1010
1001
1000
0111
then repeat?

As for the duty cycle.. Try plotting the wave forms for the clock and node 2 on squared paper or similar.

3. Jan 11, 2017

### Granger

Yes, sorry I misread the last one.

Is the frequency correct?

Also for the duty cycle, I'm not getting it I'm sorry, can you be more explicit please?

4. Jan 11, 2017

### CWatters

Yes the frequency is 14KHz.

Well start by drawing the clock waveform. Then below it draw the waveform for the 4 outputs of the counter. On the first clock edge assume it's loaded with 1100. Then on the next clock edge they become 1011 etc

I would continue plotting for a bit more than one repeat (eg draw the wave forms for 8 to 10 clock cycles.

PS I haven't actually checked that the counter is counting down.

5. Jan 11, 2017

### Granger

Thanks. So I did what you told me and obtained (naming the signal Q3Q2Q1Q0)

Q0: 010101 010101 010101 010101 010101...
Q1: 011001 011001 011001 011001 011001...
Q2: 100001 100001 100001 100001 100001...
Q3: 111110 111110 111110 111110 111110...
Now the duty-cycle should be 2/6 = 33%? Because for each signal cycle we have 2 ones and 4 zeros...

Last edited: Jan 11, 2017
6. Jan 11, 2017

### CWatters

Yes that's what I make it.

7. Jan 11, 2017

### Granger

Nice! Thank you very much for the help!