Flexible monolithic continuous-time analog low-pass filter with minimal circuitry

• US 6,344,773 B1
• Filed: 10/20/2000
• Issued: 02/05/2002
• Est. Priority Date: 10/20/2000
• Status: Expired due to Term

• Current Assignee: Analog Devices International Unlimited Company (Analog Devices, Inc.)
• Original Assignee: Linear Technology Corporation (Analog Devices, Inc.)
• Inventors: Sevastopoulos, Nello G., LaPorte, Doug A.
• Primary Examiner(s): Wells, Kenneth B.
• Assistant Examiner(s): Dinh, Paul
• Application Number:
  US09/693,058
• Time in Patent Office: 473 Days
• Field of Search: 327/552, 327/553, 327/554, 327/555, 327/556, 327/557, 327/558, 327/344, 330/260, 330/261, 330/278, 330/279, 330/280, 330/281, 330/282, 330/284, 330/285, 330/291, 330/293, 330/294
• US Class Current: 327/558
• CPC Class Codes: H03H 11/04 Frequency selective two-port networks
• CPC Class Codes: H03H 11/1291 Current or voltage controlled filters

Abstract

A completely tunable second order low-pass filter with minimal active circuitry is disclosed. The filter provides a very flexible choice of filter parameters such as cutoff frequency, DC gain, and Q factor, by selecting appropriate resistor values for a single integrated circuit with much lower capacitance, capacitance ratio, and active circuitry than other standard low-pass circuit configurations.

Claims

1. A low-pass filter circuit having an input for receiving an analog input signal V_in and having an output for producing a filtered analog output signal V_out, wherein the filter circuit has a gain, defined by a ratio of V_out to V_in, having a magnitude and a phase dependent upon frequency w, the filter circuit coupled between the input and the output for providing the magnitude, such that the magnitude as a function of frequency includes a passband to pass low frequencies and a stopband to stop high frequencies, and a cutoff frequency w₀ in a transition region therebetween, the filter circuit causing the gain to conform to a second-order frequency-dependent function expressed as:

$H_0<br><br>\frac{w_0^2}{s^2+s<br><br>\frac{w_0}{Q}+w_0^2}$

wherein s=j.w, where j represents a complex number equal to the square root of negative one, H₀ represents the DC gain of the filter circuit, and Q represents the Q factor or pole quality factor of the filter circuit, the filter circuit comprising;

a first and second resistors coupled between the input and the output;

an operational amplifier having a negative input, a positive input, and an output;

a third resistor connected between the first resistor and the negative input of the operational amplifier;

a first capacitor connected between the negative input of the operational amplifier and the output of the filter circuit;

a feedback element having an input, an output, and a negative gain forming a positive feedback path to achieve a very flexible choice of filter parameters w₀, H₀, and Q; and

a second capacitor connected between the output of the feedback element and the first resistor.

2. The low-pass filter circuit of claim 1, wherein the first capacitor, the second capacitor, the operational amplifier, and the feedback element are integrated.

3. The low-pass filter circuit of claim 1, wherein the low-pass filter circuit is a monolithic integrated circuit.

4. The low-pass filter circuit of claim 1, wherein the DC gain H₀, the cutoff frequency w₀, and the Q factor Q conform to the following equations:

$\begin{array}{c}{H}_0=-\frac{R_2}{R_1}\\ w_0=\sqrt{\frac{1}{R_2<br><br>R_3<br><br>C_1<br><br>C_2}}\\ Q=\frac{R_1<br><br>\sqrt{R_2<br><br>R_3<br><br>C_1<br><br>C_2}}{\left(R_1<br><br>R_2+R_1<br><br>R_3+R_2<br><br>R_3\right)<br><br>C_1+{\mathrm{KR}}_1<br><br>R_2<br><br>C_2}\end{array}$

wherein R1 and R2 and R3 are resistor values of the first, second, and third resistors, C1 and C2 are capacitor values of the first and second capacitors, and K is the gain of the feedback element.

5. The low-pass filter circuit of claim 1, wherein the low-pass filter may be cascaded in series to form higher order filters, wherein the higher order is equal to 2ⁿ and n is the number of cascaded low-pass filter circuits.

6. A low-pass filter circuit having an input for receiving an analog input signal V_in and having an output for producing a filtered analog output signal V_out, wherein the filter circuit has a gain, defined by a ratio of V_out to V_in, having a magnitude and a phase dependent upon frequency w, the filter circuit coupled between the input and the output for providing the magnitude, such that the magnitude as a function of frequency includes a passband to pass low frequencies and a stopband to stop high frequencies, and a cutoff frequency w₀ in a transition region therebetween, the filter circuit causing the gain to conform to a second-order frequency-dependent function expressed as:

$H_0<br><br>\frac{w_0^2}{s^2+s<br><br>\frac{w_0}{Q}+w_0^2}$

wherein s=j.w, where j represents a complex number equal to the square root of negative one, H₀ represents the DC gain of the filter circuit, and Q represents the Q factor or pole quality factor of the filter circuit, the filter circuit comprising;

a differential amplifier having a negative and a positive input, and a negative and a positive output;

a first and second resistors connected between the input of the low-pass filter circuit and the negative input of the differential amplifier;

a third and fourth resistors connected between the input of the low-pass filter circuit and the positive input of the differential amplifier;

a fifth resistor connected between the first resistor and the positive output of the differential amplifier;

a sixth resistor connected between the third resistor and the negative output of the differential amplifier;

a first capacitor connected between the negative input of the differential amplifier and the positive output of the differential amplifier;

a second capacitor connected between the positive input of the differential amplifier and the negative output of the differential amplifier;

a third capacitor connected between the first resistor and the negative output of the differential amplifier; and

a fourth capacitor connected between the third resistor and the positive output of the differential amplifier.

7. The low-pass filter circuit of claim 6, wherein the differential amplifier, the first capacitor, the second capacitor, the third capacitor, and the fourth capacitor are integrated.

8. The low-pass filter circuit of claim 6, wherein the low-pass filter circuit is a monolithic integrated circuit.

9. The low-pass filter circuit of claim 6, wherein the first and third resistors have the same resistance, the second and fourth resistors have the same resistance, and the fifth and sixth resistors have the same resistance.

10. The low-pass filter circuit of claim 6, wherein the first capacitor and the second capacitor have the same capacitance, and the third capacitor and the fourth capacitor have the same capacitance.

11. The low-pass filter circuit of claim 6, wherein the DC gain H₀, the cutoff frequency w₀, and the Q factor Q conform to the following equations:

$\begin{array}{c}{H}_0=-\frac{R_2}{R_1}\\ w_0=\sqrt{\frac{1}{R_2<br><br>R_3<br><br>C_1<br><br>C_2}}\\ Q=\frac{R_1<br><br>\sqrt{R_2<br><br>R_3<br><br>C_1<br><br>C_2}}{\left(R_1<br><br>R_2+R_1<br><br>R_3+R_2<br><br>R_3\right)<br><br>C_1-R_1<br><br>R_2<br><br>C_2}\end{array}$

where R1 is the resistance of the first and third resistors, R2 is the resistance of the fifth and sixth resistors, R3 is the resistance of the second and fourth resistors, C1 is the capacitance of the first and second capacitors, and C2 is the capacitance of the third and fourth capacitors.

12. The low-pass filter of claim 6, wherein the low-pass filter circuit may be cascaded in series to form higher order filters.

13. The low-pass filter of claim 6, wherein the low-pass filter is combined with a second circuit, the second circuit comprising:

a differential amplifier having a negative and a positive input, and a negative and a positive output;

a first resistor connected between the negative input of the differential amplifier and the positive output of the differential amplifier of the low-pass filter;

a second resistor connected between the positive input of the differential amplifier and the negative output of the differential amplifier of the low-pass filter;

a third resistor connected between the negative input and the positive output of the differential amplifier;

a fourth resistor connected between the positive input and the negative output of the differential amplifier;

a first capacitor connected between the negative input and the positive output of the differential amplifier;

a second capacitor connected between the positive input and the negative output of the differential amplifier;

a third capacitor connected between the negative input of the differential amplifier and the first resistor of the low-pass filter; and

a fourth capacitor connected between the positive input of the differential amplifier and the third resistor of the low-pass filter.

14. The low-pass filter circuit of claim 13, wherein the low-pass filter circuit and the second circuit form a third-order low-pass filter circuit with a stopband notch.

15. The low-pass filter circuit of claim 14, wherein the third-order low-pass filter circuit is a monolithic integrated circuit.