SBOA225 June 2021 OPA325 , TLV316 , TLV9062

Input | Output | Supply | |||
---|---|---|---|---|---|

V_{iMin} |
V_{iMax} |
V_{oMin} |
V_{oMax} |
V_{cc} |
V_{ee} |

–2.45V | +2.45V | 0.05V | 4.95V | 5V | 0V |

Gain | Cutoff
Frequency (f_{c}) |
Max
Frequency (f_{max}) |
V_{ref} |
---|---|---|---|

1V/V | 1kHz | 10kHz | 2.5V |

**Design Description**

The Butterworth Sallen-Key (SK) high-pass (HP) filter is a 2nd-order active filter. Vref provides a DC offset to accommodate for single-supply applications.

An SK filter is usually preferred when small Q factor is desired, noise rejection is prioritized, and when a non-inverting gain of the filter stage is required. The Butterworth topology provides a maximally flat gain in the pass band.

**Design Notes**

- Select an op amp with sufficient input common-mode range and output voltage swing.
- Add V
_{ref}to bias the input signal to meet the input common-mode range and output voltage swing. - Select the capacitor values first since
standard capacitor values are more coarsely subdivided than the resistor values. Use
high-precision, low-drift capacitor values to avoid errors in f
_{c}. - To minimize the amount of slew-induced distortion, select an op amp with sufficient slew rate (SR).
- For HP filters, the maximum frequency is set by the gain bandwidth (GBW) of the op amp. Therefore, be sure to select an op amp with sufficient GBW.

**Design
Steps**

The first step is to find component values for the normalized cutoff frequency of 1 radian/second. In the second step the cutoff frequency is scaled to the desired cutoff frequency with scaled component values.

The transfer function for the second-order Sallen-Key high-pass filter is given by:

$\text{H(s)}=\frac{{s}^{2}}{{s}^{2}+s\left(\frac{1}{{R}_{2}\times {C}_{1}}+\frac{1}{{R}_{2}\times {C}_{2}}\right)+\frac{1}{{R}_{1}\times {R}_{2}\times {C}_{1}\times {C}_{2}}}$

$\text{H(s)}=\frac{{\text{s}}^{2}}{{\text{s}}^{\text{2}}{\text{+ a}}_{1}{\text{\xd7 s + a}}_{\text{0}}}$

where,

${\text{a}}_{1}=\frac{1}{{R}_{2}\times {C}_{1}}+\frac{1}{{R}_{2}\times {C}_{2}},{a}_{0}=\frac{1}{{R}_{1}\times {R}_{2}\times {C}_{1}\times {C}_{2}}$

- Set normalized values of C
_{1}and C_{2}(C_{1n}and C_{2n}) and calculate normalized values of R_{1}and R_{2}(R_{1n}and R_{2n}) by setting w_{c}to 1 radian/sec (or fc = 1 / (2 × π) Hz). For the second-order Butterworth filter, (see the*Butterworth Filter Table*in the*Active Low-Pass Filter Design Application Report*).${\text{a}}_{0}=\text{1,}{\mathrm{a}}_{1}=\sqrt{2}\text{,}\text{let}{\mathrm{C}}_{\mathrm{1n}}={C}_{\mathrm{2n}}=1\mathrm{F,}\mathrm{then}{R}_{\mathrm{1n}}\times {R}_{\mathrm{2n}}=1\mathrm{or}{R}_{\mathrm{2n}}=\frac{1}{{R}_{\mathrm{1n}}}\mathrm{,}{a}_{1}=\frac{2}{{R}_{\mathrm{2n}}}=\sqrt{2}$${\text{\u2234 R}}_{\mathrm{2n}}=\sqrt{2}=\; 1.414\Omega ,{R}_{\mathrm{1n}}=\frac{1}{{R}_{\mathrm{2n}}}=\; 0.707\Omega $ - Scale the component values and cutoff
frequency. The resistor values are very small and capacitors values are unrealistic, hence
these have to be scaled. The cutoff frequency is scaled from 1 radian/sec to
w
_{0}. If*m*is assumed to be the scaling factor, increase the resistors by*m*times, then the capacitor values have to decrease by 1/*m*times to keep the same cutoff frequency of 1 radian/sec. If the cutoff frequency is scaled to be w_{0}, then the capacitor values have to be decreased by 1 / w_{0}. The component values for the design goals are calculated in steps 3 and 4.${\text{R}}_{1}={\text{R}}_{\mathrm{1n}}\times m\text{,}{\text{R}}_{2}={\text{R}}_{\mathrm{2n}}\times m$${\text{C}}_{1}={C}_{2}=\frac{{C}_{\mathrm{1n}}}{m\times {w}_{0}}F$ - Set C
_{1}and C_{2}to 10nF, then calculate*m*.${\text{w}}_{0}=2\times \pi \times \text{1kHz,}m=\text{15915.5}$ - Select R
_{1}and R_{2}based on*m*.${\text{R}}_{\text{1}}\text{= 0.707\xd7 15915 = 11252\u2126 \u2248 11k\u2126(StandardValue)}$${\text{R}}_{\text{2}}\text{= 1.414\xd7 15915 = 22504\u2126 \u2248 23k\u2126(StandardValue)}$ - Calculate the minimum required GBW and SR
for f
_{max}.${\text{GBW=100 \xd7 Gain \xd7 f}}_{\text{max}}\text{=100 \xd7 1 \xd7 10kHz=1MHz}$${\text{SR = 2 \xd7 \pi \xd7 f}}_{\mathrm{max}}{\text{\xd7 V}}_{\mathrm{ipeak}}\text{=2 \xd7 \pi \xd7 10kHz\xd7 2.45V=0.154}\frac{V}{\mathrm{\mu s}}$The TLV9062 device has a GBW of 10MHz and SR of 6.5V/µs, so it meets these requirements.

**Design
Simulations**

**AC Simulation Results**

**Transient Simulation Results**

The following image shows the filter output in response to a ± 2.5-V, 10-kHz input signal (gain is 1V / V).

The following image shows the filter output in response to a ± 2.5-V, 10-Hz input signal (gain is 0.014V / V).

**Design References**

- See Analog Engineer's Circuit Cookbooks for TI's comprehensive circuit library.
- SPICE Simulation File - SBOMB38.
- TI Precision Labs

**Design Featured Op Amp**

TLV9062 | |
---|---|

Vss |
1.8V to 5.5V |

VinCM |
Rail-to-Rail |

Vout |
Rail-to-Rail |

Vos |
0.3mV |

Iq |
538µA |

Ib |
0.5pA |

UGBW |
10MHz |

SR |
6.5V / µs |

#Channels |
1, 2, 4 |

www.ti.com/product/TLV9062 |

**Design Alternate Op Amp**

TLV316 | OPA325 | |
---|---|---|

Vss |
1.8V to 5.5V | 2.2V to 5.5V |

VinCM |
Rail-to-Rail | Rail-to-Rail |

Vout |
Rail-to-Rail | Rail-to-Rail |

Vos |
0.75mV | 0.150mV |

Iq |
400µA | 650µA |

Ib |
10pA | 0.2pA |

UGBW |
10MHz | 10MHz |

SR |
6V / µs | 5V / µs |

#Channels |
1, 2, 4 | 1, 2, 4 |

www.ti.com/product/OPA316 | www.ti.com/product/OPA325 |