I need to simulate a waveform generator using Multisim. I used the design in this Link. the frequency is 1KHz.
It works fine but I need some modifications:
1. I need the peak to peak voltage(Vpp) to be changeable so I did this 
I got the right Vpp but the frequency decreased to about quarter of its original value. why did the frequency change?
2. I need to be able to change the duty cycle while keeping the same frequency so I did this modification 
But unfortunately the frequency went up to 1.5KHz and the duty cycle wasn't the calculated value ( 2/12 )
For both issues, I am asking for an explanation and if there is a better way to do them.
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The frequency reduced when you added the zener clamps because the "aiming" voltage for the integrator reduced i.e. the voltages at the input to the integrator determines the rate at which the capacitor can charge or discharge - lower the voltage (by clamping it) and frequency naturally reduces.
For the 2nd scenario where you are trying to make the integrator charge at different rates depending on the input polarity, the average value of R2 and R5 should equal R2 in the previous circuit. Clearly this is not the case because in the original circuit R2 was 11k while the new circuit has R2 at 2k and R5 at 10k (average is 6k). Given that diodes won't be perfect (i.e. possess some volt drop when forward conducting), there will be other errors to consider.
Why not just try the following circuit - note the "symmetry" pot: -
Also, get rid of the 741 op-amp if you want decent performance at higher audio frequencies.
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\$\begingroup\$ OK, keeping the average of the resistors solved the problem. you say 741 is not good at high frequencies. what do you suggest instead ? \$\endgroup\$ Commented Feb 2, 2016 at 14:48
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\$\begingroup\$ Virtually any op-amp is better than a 741 - look for one with a specified gain-band-width-product in the 10 MHz range. FYI a 741 is 1MHz but when used as a comparator (U1) in your circuit it is very slow at recovering from hitting the end stops as it switches. If you are happy to go surface mount then the AD8671 (single) or 72 (dual) or 74 (quad) is very good and will work down to a +/-5V supply. \$\endgroup\$– Andy akaCommented Feb 2, 2016 at 14:54