Ideal Transfer Function
The Ideal Straight-Line Transfer Function of an ADC is a straight line from the minimum input voltage (voltage reference low; VREFL) to the maximum input voltage (voltage reference high; VREFH). The Ideal Transfer Function is then quantized (divided into steps) by the number of codes the ADC is capable of resolving. The input voltage range is divided into steps, each step having the same width.
This Ideal Code Width (ICW) — also known as 1LSB — is:
ICW = 1LSB = (VREFH – VREFL)/2N
Where:
N is the “width” of the ADC, in our examples, 10 bits.
The Ideal Transfer Function is then:
Code = (VIN – VREFL) / 1LSBVIN = (Code*1LSB) + VREFL
Quantization Error (EQ) and Method
The way the Ideal transfer function is divided into steps depends on the method of quantization the ADC uses. The two possible methods are:
Most ADC’s exhibit some non-linearity at the endpoints due to the difficulty in measuring a signal that is identical to the reference. If these errors are accounted for, a more accurate portrayal of the ADC behavior in application is possible. For this reason, the Adjusted Straight-Line Transfer Function is drawn between the minimums input voltage plus the Zero-Scale Error (VREFL + EZS) to the maximum input voltage plus the Full- Scale Error (VREFH + EFS).
The Adjusted Transfer Function is then quantized in the same method as the Ideal Transfer Function. The Adjusted Code Width is therefore:
ACW = [(VREFH + EFS) – (VREFL + EZS)] / 2N
The Adjusted Transfer Function is then:
Code = (VIN – VREFL – EZS) / ACW VIN = (Code*ACW) + VREFL + EZS
The Ideal Straight-Line Transfer Function of an ADC is a straight line from the minimum input voltage (voltage reference low; VREFL) to the maximum input voltage (voltage reference high; VREFH). The Ideal Transfer Function is then quantized (divided into steps) by the number of codes the ADC is capable of resolving. The input voltage range is divided into steps, each step having the same width.
This Ideal Code Width (ICW) — also known as 1LSB — is:
ICW = 1LSB = (VREFH – VREFL)/2N
Where:
N is the “width” of the ADC, in our examples, 10 bits.
The Ideal Transfer Function is then:
Code = (VIN – VREFL) / 1LSBVIN = (Code*1LSB) + VREFL
Quantization Error (EQ) and Method
The way the Ideal transfer function is divided into steps depends on the method of quantization the ADC uses. The two possible methods are:
- Uncompensated Quantization — The first step is taken at 1LSB, with each successive step taken at 1LSB intervals and the last step taken at VREFH – 1LSB. The Quantization Error (EQ) in this case is from 0LSB to 1LSB.
- ½LSB Compensated Quantization – The first step is taken at 1⁄2LSB, with each successive step taken at 1LSB intervals and the last step taken at VREFH – 11⁄2LSB. The Quantization Error (EQ) in this case is ±1⁄2LSB
Most ADC’s exhibit some non-linearity at the endpoints due to the difficulty in measuring a signal that is identical to the reference. If these errors are accounted for, a more accurate portrayal of the ADC behavior in application is possible. For this reason, the Adjusted Straight-Line Transfer Function is drawn between the minimums input voltage plus the Zero-Scale Error (VREFL + EZS) to the maximum input voltage plus the Full- Scale Error (VREFH + EFS).
The Adjusted Transfer Function is then quantized in the same method as the Ideal Transfer Function. The Adjusted Code Width is therefore:
ACW = [(VREFH + EFS) – (VREFL + EZS)] / 2N
The Adjusted Transfer Function is then:
Code = (VIN – VREFL – EZS) / ACW VIN = (Code*ACW) + VREFL + EZS
