# What does "great linearity" means for a ring oscillator?

#### littlerock

Joined Feb 9, 2018
4
Hello all. I just want to ask the significance or meaning of the phrase "good linearity" or "great linearity" as an advantage for the design of a ring oscillator. I am reading a paper about a bootstrapped ring oscillator and it says that "the proposed ring oscillator provides great linearity while the ring oscillator is controlled by power supply regulation". What does it mean?

#### dl324

Joined Mar 30, 2015
15,462
Post more the text from the paper so we can have some context.

#### littlerock

Joined Feb 9, 2018
4
Post more the text from the paper so we can have some context.
The Abstract of the paper is this:

"An ultra-low-power ring oscillator is presented in this paper. A bootstrapped CMOS delay cell is proposed to operate at 0.2 V - 0.6 V power supply. The proposed delay cell provides a boosted voltage swing to enhance the driving capability of the delay cell. Besides, the bootstrap technique suppresses the serious process variation in the low-voltage-supply design. As compared with conventional inverter-based ring oscillator, the proposed ring oscillator provides great linearity while the ring oscillator is controlled by power supply regulation. A test chip is
fabricated in the 90nm SPRVT Low-K CMOS process. Chip measurement results demonstrate that the proposed bootstrapped
ring oscillator can achieve 46 MHz at 0.2 V and 773 MHz at 0.6 V power supply. A 0.5 V 400 MHz ADPLL is verified in the test chip as well. The power consumption at 400 MHz operating clock is only 70 uW. The peak-to-peak jitter is 69.1 ps."

#### MrChips

Joined Oct 2, 2009
27,695
Linearity refers to the mathematical relationship between two parameters.
The fundamental equation of a straight line is:

y = mx + c

x = independent variable
y = dependent variable

in other words, y is dependent on x.
m = slope of the line (or gain of the relationship, m = y/x approx.)
c = is the offset

Generally, both m and c are constants. They do not change.
In particular, pertaining to your question, if m is constant, then the relationship between y and x is perfectly linear.

In real life, m may vary somewhat. That would determine the difference between "good linearity" and "great linearity".

What they are referring to is relationship between a control voltage and the resultant frequency of the oscillator. This would be called a voltage controlled oscillator.

• littlerock

#### littlerock

Joined Feb 9, 2018
4
Linearity refers to the mathematical relationship between two parameters.
The fundamental equation of a straight line is:

y = mx + c

x = independent variable
y = dependent variable

in other words, y is dependent on x.
m = slope of the line (or gain of the relationship, m = y/x approx.)
c = is the offset

Generally, both m and c are constants. They do not change.
In particular, pertaining to your question, if m is constant, then the relationship between y and x is perfectly linear.

In real life, m may vary somewhat. That would determine the difference between "good linearity" and "great linearity".

What they are referring to is relationship between a control voltage and the resultant frequency of the oscillator. This would be called a voltage controlled oscillator.
Thanks for the response MrChips. Now, I understand. 