How to choose analog-signal-chain components: part 4

Op amps find use in second-order filters and instrumentation amplifiers.

In part 3 of this series, we described using the op amp to build some single-pole filters.

Figure 1. The two-capacitor Sallen-Key topology implements a second-order low-pass filter.

Q: How do we build higher-order filters?
A: Figure 1 shows one approach to a low-pass filter using the Sallen-Key topology. With two capacitors, it’s a second-order filter.

Q: How do we choose the component values for a specific cutoff frequency?
A: That depends on what type of filter we want to design. Table 1 lists several types from which we can choose, depending on our preferences for optimizing phase response and group delay, passband magnitude flatness, roll-off, or ripple.

Filter Type	Characteristic
Bessel	Maximally linear phase response with constant group delay
Butterworth	Maximally flat magnitude in the passband
Chebyshev Type 1	Steep roll-off, some ripple in the passband
Chebyshev Type 2	Steep roll-off, some ripple in stopband

Table 1. Filter types and characteristics.

Once we have chosen, we can take advantage of online filter-design tools to do the math for us. Table 2 lists three:

Company	Filter design tool link
Analog Devices	https://tools.analog.com/en/filterwizard/
Microchip Technology	https://filterlab.microchip.com/filter
Texas Instruments	https://webench.ti.com/filter-design-tool

Table 2. Online op-amp filter design tools.

Q: How do they work?
A: First, they ask whether you want a low-pass, high-pass, bandpass, or bandstop filter. Then they take you to a page that lets you specify cutoff frequency, ripple, DC gain, and filter type. In Figure 2, I’ve chosen a low-pass 1-kHz Butterworth filter:

Figure 2. A filter-design tool allows you to enter parameters such as cutoff frequency. Source: Texas Instruments Filter Design Tool.

Then, I click Select, and the tool adds component values to our Figure 1 Sallen-Key circuit (Figure 3):

Figure 3. The design tool calculates passive-component values. Source: Texas Instruments Filter Design Tool.

Q: Wait, so is this a Butterworth filter or a Sallen-Key filter?
A: It’s a Butterworth filter implemented using a Sallen-Key topology. The Butterworth filter can be implemented in other analog topologies or digitally. The key is that the Butterworth response follows this equation, where n equals the filter order:

Figure 4 plots this transfer function and compares it with a Chebyshev Type 1 second-order filter response.

Q: What else should I know about op amps?
A: For test-and-measurement applications, the instrumentation amplifier is a useful tool. As shown in Figure 5, it consists of two buffers and a differential amplifier, as we discussed in part 2, and you can build one yourself. However, you can also buy a packaged version and let the vendor address issues such as impedance matching.

Q: How does it work?
A: The differential amplifier provides common-mode rejection. Since all the associated resistors R_D in Figure 5 are equal, the differential amplifier’s gain is one, and V_OUT= V₃–V₄. Note, though, that the input impedance of the differential stage is low, even with an ideal op amp. If R_D equals 10 kW, the differential-stage input impedance is 20 kW. So, we add the buffers to provide high input impedance, which is useful for measuring signals from sensors with high output impedances.

Q: What’s R_GAIN?
A: That’s an external resistor you add to set gain. To see the resistor’s effect on gain, we can calculate the current through it:

We can also express I_GAIN in terms of V₁ and V₂ (keeping in mind that the voltage at each buffer’s inverting input must equal the voltage at its noninverting input for the device to operate in the linear range):

Then we can calculate the transfer function:

Q: What are some other types of amplifiers?
A: So far, we have discussed voltage-in/voltage-out op amps. In contrast, transimpedance amplifiers have current inputs and voltage outputs, and transconductance amplifiers have voltage inputs and current outputs. We’ll conclude this series next time with a look at these devices and their applications.