Are low leakage multiplexers important in high impedance PLC systems?

An enthusiastic young engineer working for a leading programmable logic controller (PLC) manufacturer is designing a multi-channel 24-bit analog input module that accepts inputs from high-impedance sensors. He chose a Texas Instruments 24-bit delta-sigma analog-to-digital converter (ADS125H02), a 5-V reference, and a Texas Instruments precision amplifier ( OPA192 ).
When choosing a multiplexer, he had three options: a MUX36D04 from Texas Instruments and two multiplexers from other vendors (MUX2 and MUX3). Each of the multiplexer specifications is similar, except that the input leakage current specifications are 1 pA, 100pA, and 1 nA (typical at 25°C).
At first, the engineer thought that the three multiplexers looked identical, and that the input leakage current in the three multiplexers was negligibly low. He thinks it's possible to choose any of the three and get similar performance from his system.
In this blog post, you will find that he may have overlooked the leakage current of the multiplexer.
Figure 1 shows a standard block diagram of a data acquisition system with multiple sensor interfaces.

Leakage Current: Silently Cancelling Offset Errors Leakage current is an important parameter because it contributes to DC errors both when the switch is turned on and off. The multiplexer datasheet has many specifications related to leakage current, including the leakage current flowing through the source pin (IS) or the drain pin (ID) when the switch is closed or open. Figure 2 shows a simplified model of an analog switch.
Figure 2: Simplified Small Signal Model with Switch Open

As shown in Figure 2, the output voltage VOUT is usually connected to the non-inverting terminal of the op amp, which has a high impedance. So for simplicity, the engineer ignores the effect of the load resistance RL. RO is the on-resistance of the switch.
When the switch is closed, Equation 1 calculates the voltage error introduced by the leakage current:
When the switch is open, leakage current flows through the respective terminal (drain or source) and introduces an offset error at the output.
Figure 3: Simplified small-signal model with switch open

The leakage current also increases with increasing temperature. All data sheets should include typical curves for leakage current versus temperature. Although the amount of leakage current is small, it is a very important parameter when dealing with high input impedance sensors. So let's see how this parameter affects system performance.
There is actually a difference between picoamps or nanoamps of leakage current
Analog input modules in PLC systems often switch high input impedance sensors such as pH, optics, humidity, accelerometers, and chemical sensors. All of these sensors have input impedances ranging from a few hundred kiloohms to several gigaohms. Take a typical light sensor as an example, as shown in Figure 4.
Figure 4: Simplified model of a light sensor

As shown in Figure 4, the size of the shunt resistance Rsh varies from several hundred kiloohms to several gigaohms, and is inversely proportional to temperature. Since the size of the shunt capacitance is a few picofarads, it is not important, so it is not shown in Figure 4.
The effect of leakage current on system accuracy In simple terms, the sensor impedance Rsh is assumed to be 1MΩ. For a 24-bit system referenced to 5V, Equation 2 calculates the minimum resolution or voltage corresponding to 1 least significant bit (LSB) as follows:

Remember that the engineer has three multiplexers to choose from, labeled MUX36D04, MUX2, and MUX3 in Table 1. Also keep in mind that leakage current at (25°C/85°C) is the only differentiating factor. For each multiplexer, leakage current flows through the input impedance, causing offset errors that affect overall system accuracy. Table 1 briefly describes how the multiplexer affects measurement accuracy.
Most sensors have low output voltages. Any additional offset introduced due to the input stage will limit the maximum full-scale voltage range that the ADS125H02 can see. As can be seen from Table 1, for a high-precision data acquisition system, even a few hundred picoamps of input leakage can have a significant impact on measurement accuracy. Leakage current varies with temperature, and Table 1 shows the change in offset error at 25°C and 85°C. The light sensor impedance also varies with light intensity and ambient temperature, so this can lead to not only offset errors, but also linearity errors.

So engineers can't ignore leakage current, so they need to choose a low leakage multiplexer.
Designing multi-channel analog input modules that accept high-impedance inputs presents a number of challenges. Texas Instruments' MUX36S08 and MUX36D04 ultra-low leakage analog multiplexers eliminate the need to calibrate offset errors, simplifying the design of analog input modules while also greatly reducing offset and linearity errors. The MUX36S08 and MUX36D04 feature ultra-low leakage current of 1pA at 25°C. Figure 5 shows the leakage current of the MUX36S08 as a function of temperature. (See the MUX36S08 datasheet for a detailed graph from -40°C to 125°C.)

In conclusion, the engineer cannot ignore the leakage current, so he must choose the low leakage multiplexer from Texas Instruments. The MUX36S08 and MUX36D04 options address the need for low leakage while also offering low capacitance, low charge injection, rail-to-rail operation and low power consumption