8.2.1.1 Design Requirements

In this example it is required to design a bandpass filter with band-pass frequency of 10 kHz, and a center frequence of approximately 10% from the total frequence of the filter. This is achieved by cascading two band-pass filters, A and B, with slightly different center frequencies.

8.2.1.2 Detailed Design Procedure

The center frequency of the separate band-pass filters A, and B can be calculated by Equation 16:

Equation 16.

where

• C = 33 nF
• R1 = 2 KΩ
• R2 = 6.2 KΩ
• and R3 = 45 Ω

This gives Equation 17 for filter A:

Equation 17.

and Equation 18 for filter B with C = 27nF:

Equation 18.

Bandwidth can be calculated by Equation 19:

Equation 19.

For filter A, this gives Equation 20:

Equation 20.

and Equation 21 for filter B:

Equation 21.

8.2.1.3 Application Curve

The responses of filter A and filter B are shown as the thin lines in Figure 39; the response of the combined filter is shown as the thick line. Shifting the center frequencies of the separate filters farther apart, results in a wider band; however, positioning the center frequencies too far apart results in a less flat gain within the band. For wider bands more band-pass filters can be cascaded.

Figure 39. Active Band-Pass Filter Curve

8.2.2.1 Design Requirements

In this example, it is desired to measure a current between 0 A and 2 A using a sense resistor of 100 mΩ, and convert it to an output voltage of 0 to 5 V. A current of 2 A flowing through the load and the sense resistor results in a voltage of 200 mV across the sense resistor. The op amp amplifies this 200 mV to fit the current range to the output voltage range.

8.2.2.2 Detailed Design Procedure

To measure current at a point in a circuit, a sense resistor is placed in series with the load, as shown in Figure 40. The current flowing through this sense resistor results in a voltage drop, that is amplified by the op amp. The rail-to-rail input and the low V_OS features make the LMV84x ideal op amps for high-side, current-sensing applications.

The input and the output relation of the circuit is given by Equation 22:

For a load current of 2 A and an output voltage of 5 V the gain would be V_OUT / V_SENSE = 25.

If the feedback resistor, R_F, is 100 kΩ, then the value for R_G is 4 kΩ. The tolerance of the resistors has to be low to obtain a good common-mode rejection.

8.2.3.1 Design Requirements

In this example it is desired to measure temperature in the range of 0°C to 500°C with a resolution of 0.5°C using a K-type thermocouple sensor. The power supply for both the LMV84x and the ADC is
3.3 V.

8.2.3.2 Detailed Design Procedure

A thermocouple is a junction of two different metals. These metals produce a small voltage that increases with temperature. A K-type thermocouple is a very common temperature sensor made of a junction between nickel-chromium and nickel-aluminum. There are several reasons for using the K-type thermocouple. These include temperature range, the linearity, the sensitivity, and the cost.

A K-type thermocouple has a wide temperature range. The range of this thermocouple is from approximately −200°C to approximately 1200°C, as can be seen in Figure 42. This covers the generally used temperature ranges.

Over the main part of the range the behavior is linear. This is important for converting the analog signal to a digital signal. The K-type thermocouple has good sensitivity when compared to many other types; the sensitivity is 41 µV/°C. Lower sensitivity requires more gain and makes the application more sensitive to noise. In addition, a K-type thermocouple is not expensive, many other thermocouples consist of more expensive materials or are more difficult to produce.

Figure 42. K-Type Thermocouple Response

The temperature range of 0°C to 500°C results in a voltage range from 0 mV to 20.6 mV produced by the thermocouple. This is shown in Figure 42.

To obtain the best accuracy the full ADC range of 0 to 3.3 V is used and the gain needed for this full range can be calculated Equation 23:

If R_G is 2 kΩ, then the value for R_F can be calculated with this gain of 160. Because A_V = R_F / R_G, R_F can be calculated in Equation 24:

To achieve a resolution of 0.5°C a step smaller than the minimum resolution is needed. This means that at least 1000 steps are necessary (500°C/0.5°C). A 10-bit ADC would be sufficient as this gives 1024 steps. A 10-bit ADC such as the two channel 10-bit ADC102S021 would be a good choice.

At the point where the thermocouple wires are connected to the circuit on the PCB unwanted parasitic thermocouple is formed, introducing error in the measurements of the actual thermocouple sensor.

Using an isothermal block as a reference will compensate for this additional thermocouple effect. An isothermal block is a good heat conductor. This means that the two thermocouple connections both have the same temperature. The temperature of the isothermal block can be measured, and thereby the temperature of the thermocouple connections. This is usually called the cold junction reference temperature. In the example, an LM35 is used to measure this temperature. This semiconductor temperature sensor can accurately measure temperatures from −55°C to 150°C.

The ADC in this example also coverts the signal from the LM35 to a digital signal, hence, the microprocessor can compensate for the amplified thermocouple signal of the unwanted thermocouple junction at the connector.