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# Ramps linearity vs resolution

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#### ruby1212

##### Junior Member level 3
Hello all,
Can anyone share a comprehensive point of view about the definition of Linearity and Resolution of a ramp ?
Saying that a ramp is 12bits linear or has a resolution of 12 bits are equivalent descriptions ? What does linearity/resolution physically mean ?
Also what does accuracy/precision of a ramp stand for ??? Are they different from the linearity and resolution properties ?

Linearity describes how much the ramp deviates from a perfectly linear (straight line). How well you measure this linearity depends upon the precision and accuracy.

Resolution is basically the same as precision. It's the smallest measurement increment (such as 1 out of 12 bits, or say 1mV) that you would use to measure the ramp voltage (or linearity).

Accuracy is the absolute accuracy of the measurement. For example, your measurement precision may be 1 of of 12 bits, but the accuracy may be only 3 out of 12 bits (due to inaccuracies in the circuit gains and the A/D conversion process).

ruby1212

### ruby1212

Points: 2
An accurate ramp specified as 1V per microsecond, may actually be 1.01V some times , drifting to .99 V in a micro second. A precision ramp is specified as 1V per micro second but it is actually .95V, but it never alters.
We used a video waveform with a line rate ramp on it to adjust the linearity correctors in TV transmitters. You can see the sawtooth curve up or down as you altered the controls. But to actually measure the result we used a staircase waveform, then passed the output signal through a special differentiating filter which displayed each step as a pulse. We then measure the amplitudes of the pulses, the largest was set to 100% on a CRO, we then read the difference as a pecentage , which was typically 3%. o the dynamic range was split into 5 steps of 100, each of which we could measure to 1%. If you passed the ramp through this filter you could see a very small almost horizontal wave form, which was the differentiated saw tooth, which could be used for measuremennt, but the results need to be looked at carefully.
Frank

ruby1212

### ruby1212

Points: 2
Ok. Thnaks for your replies Crutschow and Chuckey. What would you say about the generation of a ramp on chip ? I mean for example if i simulate a circuit that generates a ramp in Cadence how would i characterise it's linearity and resolution in "bits" ? I understand that the linearity is the amount of deviation compared to a straight line, but how does it translate to "bits" ? How can i know whether my ramp will be more or less accurate or precise once realised in silicium ?

Linear -- is like the rate at which the amplitude changed should be a constant from lower amplitude to maximum

ruby1212

### ruby1212

Points: 2
The number of "bits" would be related to how you define the linearity. If it's the maximum deviation from a straight line, then you would divide that deviation value by the ramp amplitude, and use that to determine the LSB this would correspond to. For example if the maximum deviation was 1mV of a 1V ramp, then the equivalent LSB is 1/1000 or slightly more than one bit out of 10 bits.

How well it works in silicon depends upon how accurate your circuit models are for the semiconductor process you are using.

ruby1212

### ruby1212

Points: 2
The number of "bits" would be related to how you define the linearity. If it's the maximum deviation from a straight line, then you would divide that deviation value by the ramp amplitude, and use that to determine the LSB this would correspond to. For example if the maximum deviation was 1mV of a 1V ramp, then the equivalent LSB is 1/1000 or slightly more than one bit out of 10 bits.

How well it works in silicon depends upon how accurate your circuit models are for the semiconductor process you are using.

Thanks for this clear response. So basically a 14bit linear ramp means that the maximum deviation from a straight line will be less than 1/2^14 Volts. Grazie!

Thanks for this clear response. So basically a 14bit linear ramp means that the maximum deviation from a straight line will be less than 1/2^14 Volts. Grazie!
Yes, but only if your D/A generation is accurate to 1 bit out of 14 (which depends upon the converter design).

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