Test & measurement
designing a second-order, 0.5Hz cutoff frequency SFG low-pass Butterworth filter: • One 10kΩ resistor •One 39pF capacitor •One 1N4001 diode
•X For simplicity of this example, select Rs = 1Ω, Cn = 1F.
•X Select Fs = 0.5Hz to maximise rejection of broadband noise. Ws = 2 × π × 0.5 = 3.141rad.
Figure 8. Filter amplitude response examples.
designing LPF based on the Butterworth topology can achieve flat band-pass and steep attenuation.
ACTIVE LOW-PASS FILTER DESIGN TECHNIQUE
A signal flow graph is a graphical representation of a system derived from a set of linear equations.2 An SFG provides a bridge from a transfer function to a corresponding circuit topology of a system.2 This theory can be applied to designing analogue filters based on active circuitry. The key advantage of an SFG filter design approach is that the damping factor, Q, and cutoff frequency can be individually controlled. An SFG LPF can help to attenuate noise and improve SNR, but comes at the cost of additional bill of material (BOM) expenses, PCB area, and power. Furthermore, an SFG LPF can affect the reference output voltage with temperature leading to a small PPM error and hence dc accuracy degradation. Figure 9 shows an example of second-order low-pass filter transitioning from transfer function to circuit blocks via the SFG method. The scaling resistor (R) and capacitor (C) configures for the cutoff frequency (please see Equation 5).
For more details about signal flow graph theory, please refer to Feedback Control of Dynamic Systems, published by Addison-Wesley.
where
Rs is scaling factor Cn is scaling factor Ws is cutoff frequency (Rad/s) The following is a calculation example for
INTRODUCING LTC6655LN Considering the RC LPF and SFG LPF trade- offs, a better solution is to have a low-pass filter placed before the integrated low noise buffer of the voltage reference as shown in Figure 10. This implementation will not only reduce the PCB area but also not hinder the voltage reference buffer response. Using a voltage reference buffer with fast settling, high input impedance, and the capability to sink and source current will help overcome poor load regulation, maintain dc accuracy, and improve transient performance. The LTC6655LN takes advantage of this architecture. It comes with a noise reduction pin that enables reduction of wideband noise and an integrated output stage buffer. LTC6655LN is internally
Table 2. The 3dB Cutoff Frequencies for Different Values of the Capacitor Connected to the NR Pin
CNR 2.500 4.096 5.000 V 0.1µF 5305 4233 3969 Hz 1µF
531
10µF 53 100µF 5.3
423 397 Hz 42.3 39.7 Hz 4.2
4.0 Hz Figure 10. LTC6655LN block diagram. Figure 9. Active RC low-pass filter implementation based on SFG method. 44
TEST CIRCUIT DESCRIPTION The AD7177-2 precision ADC was used to benchmark the performance of LTC6655/ LTC6655LN with a 10µF NR capacitor and LTC6655 followed by an active SFG filter. The AD7177-2 is a high resolution, 32-bit, low noise, fast settling, 2-channel/4-channel, sigma-delta, analogue-to-digital converter for low bandwidth inputs. AD7177-2 is integrated with a programmable digital low-pass filter that allows users to control the output data rate (ODR) from 5SPS to 10kSPS. The components used in designing SFG LPF (Figure 11) were two ADA4522-1 op amps, an AD797 op amp, 25ppm surface-mount resistors, multilayer surface-mount ceramic capacitors, and a 10µF WIMA film capacitor. ADA4522 is a rail-to- rail output op amp with a broadband noise density of 5.8nV/√Hz and 177nVp-p flicker noise. AD797 is a low noise op amp with 0.9nV/√Hz broadband noise, 50nVp-p flicker noise, excellent slew rate of
May 2025 Instrumentation Monthly
•X Set the damping factor Q = 0.71. Select this value to achieve a flat band-pass and steep attenuation to reflect Butterworth topology. •X R, C, and Rq values were chosen based on an iterative process to achieve low thermal noise and the availability of component values for surface mount.
equipped with R3 resistor (see Figure 10) and allows users to connect external capacitor at the noise reduction (NR) pin to create a low-pass filter. With LTC6655LN architecture, users can configure the low-pass cutoff frequency based on their system requirements.
The LTC6655LN RC LPF is connected to the non-inverting node of the buffer, which is the most sensitive pin on this device. Precaution must be taken when selecting a low leakage type for the external capacitor to prevent leakage current flow through the R3 resistor, which can degrade dc accuracy. Furthermore, the variation of R and C do not track each other and therefore the RC time constant and LPF cutoff frequency can change due to process, voltage, and temperature (PVT) variation.
Table 3. Resistance Value of R3 for the Three Voltage Options
Voltage Option
2.500V 4.096V 5.000V R3 ±15% 300Ω 376Ω 401Ω
A voltage reference such as the LTC6655LN with an internally built-in LPF provides the best solution in simplifying noise filter design and eliminating the need for external buffer to drive ADC voltage reference circuitry.
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