AN-1392: How to Calculate Offset Errors and Input Impedance in ADC Converters with Chopped Amplifiers (Rev. 0) PDF

AN-1392
APPLICATION NOTE
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How to Calculate Offset Errors and Input Impedance in ADC Converters with
Chopped Amplifiers
By Miguel Usach
INTRODUCTION
Integrated buffers and amplifiers in analog-to-digital converters
(ADCs) are typically chopped. An example of this implementation
of chopping can be found in the AD7124-8 and the AD7779 data
sheets. This chopping technique is required to minimize offset
and flicker noise (1/f) of the amplifier, as the CMOS transistors
are noisy and hard to match compared to other processes like a
bipolar process. By chopping the amplifier, the 1/f and offset are
translated to higher frequencies, as shown in Figure 1.
FLICKER
NOISE
nV√Hz
If the current meter connects to one of the voltage rails, the
measured current can be higher than the specifications in a data
sheet because of the input voltage headroom.
INPUT CURRENT VS. INPUT IMPEDANCE
The input impedance specification does not help accurately
calculate the error in the dc because the main contributor is the
input bias current compared to the load effect introduced by the
internal ADC input impedance.
FREQUENCY
FREQUENCY
14020-001
There are two specifications related to the input bias current:
absolute and differential.
Figure 1. Flicker Noise (1/f) Against Chopping
During the chopping transitions, there are peaks of current due
to the charge injection of the switches that generate drops or peaks
in any direction (sink and/or source) of the voltage applied to the
inputs of the ADC. The voltage drops are proportional to the
output impedance of the transducer or sensor connected to the
input of the ADC.
The absolute value (IABSOLUTE) is the input current measured in
any of the analog input pins. The differential input current
(IDIFFERENTIAL) is the current difference measured between the
analog input pin pair. This only applies to differential input ADCs.
HOW TO CALCULATE THE DC ERROR
The input current generates an offset voltage (VOFFSET) that is
directly dependent on the impedance connected to the input pin.
Generally, as shown in Figure 3, the offset generated is
VOFFSET = IABSOLUTE × R
AVERAGE CURRENT VALUE
Generally, data sheets do not provide the peak of the current
because it is difficult to measure and does not add any relevant
information. The information is not relevant because the chopping
frequency of the buffer is at a higher frequency than the input
signal bandwidth of the ADC. Consequently, any low-pass filter
added to the input pins to eliminate frequencies or tones above
the Nyquist frequency, or to reduce coupled noise, averages the
peak current, as shown in Figure 2.
14020-002
CURRENT
TIME
I
V
VADC = V ± IABSOLUTE × R
Figure 3. Voltage Drop due to Leakage Current
If the analog input pin is driven by a low impedance source like
an operational amplifier, the error is not noticeable.
The error measured by the ADC depends on the type of input
signal applied, such as a true differential input signal or a pseudo
differential/single-ended input signal.
ADC
Figure 2. Input Current vs. Time
ADC
R
14020-003
nV√Hz
FLICKER
NOISE
Measure the input current with a current meter, connecting one
terminal to VDD/2 and another terminal to the analog input
pin of the ADC.
In the case of a true differential input signal, assuming a perfect
input resistance (R) match, the error measured by the ADC is
due to the differential input current between the analog input
pin pair as described in the following equation:
VADC = V ± IDIFFERENTIAL × R
where VADC is the ADC input voltage.
Rev. 0 | Page 1 of 2
AN-1392
Application Note
R
R
R
R
14020-006
14020-004
V
Figure 4. Differential Input ADC
If the resistances do not perfectly match, the resistance mismatch
generates an error in addition to the differential input current
contribution.
In general, assuming a 1% tolerance resistance, the worst case
scenario is defined as,
VOFFSET = 2 × IABSOLUTE × 1% R + IDIFFERENTIAL × (R)
Figure 6. Pseudo Differential ADC
THE AC ERROR
The ac component directly depends on the input impedance
specification. The input impedance can be resistive or capacitive.
If the input impedance is capacitive, calculate the impedance at
the given frequency as
ZC 
In the case of pseudo differential/single-ended input signal,
there are two scenarios:

One of the analog inputs connects to a low impedance
source (see Figure 5). The error is defined as
VOFFSET = R × IABSOLUTE
R
14020-005
V
Figure 5. Pseudo Differential/Single-Ended ADC

Both inputs connect to a high impedance source (see
Figure 6). The error is the same as when using a true
differential signal.
1
2    C IN  f IN
where:
ZC is the input impedance.
CIN the input capacitance stated in a data sheet.
fIN is the input frequency.
As an example, assuming an 8 pF capacitance with an input
bandwidth of 1 kHz, the minimum input impedance is
about 20 MΩ.
MINIMIZING ERRORS
To minimize errors due to resistor mismatches in low-pass
filters, it is preferable to use small resistors and large capacitors, as
the offset and the Johnson noise generated in the resistor is lower.
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