Designing a Twin T Notch Filter in LTspice: Band Stop Tutorial

A band stop filter is created by combining an RC low pass filter with an RC high pass filter, functioning to block or severely attenuate frequencies within a specific range while passing all others. Also called a band reject or notch filter, it operates as the inverse of a band pass filter. The filter is second-order with two cutoff frequencies (-3 dB points) defining a wide stop band. It passes frequencies below the lower cutoff (f_low) and above the upper cutoff (f_high), while rejecting frequencies in between. When the stop band is extremely narrow and highly attenuated, it becomes a noise filter. The geometric mean of the cutoff frequencies determines the center frequency, and the Q factor represents the ratio of center frequency to bandwidth.

A band reject filter (band stop filter or notch filter) is an electronic circuit that blocks signals within a specific frequency range while allowing signals outside that range to pass through. The ideal transfer function magnitude |H(jω)| shows pass bands at frequencies below ωC1 and above ωC2 with |H(jω)| = 1, and a stop band between ωC1 and ωC2 with |H(jω)| = 0. Practical applications include removing power supply interference (50 Hz or 60 Hz hum) from electronic devices and audio systems. A notch filter is a highly tuned version of a band reject filter designed to eliminate a single specific frequency.

Band-stop filters exhibit a frequency response with a notch at the center frequency where the gain drops to zero. The filter allows low frequencies to pass through and high frequencies to pass through, while blocking a specific middle frequency band. The frequency response is discontinuous, which is why bandwidth is not defined for band-stop filters. The notch filter is a special case where rejection occurs at a single specific frequency rather than a band.

This section provides a comprehensive overview of filter classification and band-stop filter design principles. Filters are classified based on their frequency response characteristics: Low-pass filters pass low frequencies and attenuate high frequencies. High-pass filters pass high frequencies and attenuate low frequencies. Band-pass filters pass a specific frequency band while attenuating frequencies outside this band. Band-stop (notch) filters attenuate a specific frequency band while passing frequencies outside this band. All-pass filters pass all frequencies with unity magnitude but introduce phase shift. For a band-stop filter, both low and high frequencies are passed while a specific band is attenuated. The transfer function for a second-order band-stop filter is T(s) = (s² + ω₀²)/(s² + (ω₀/Q)s + ω₀²). At both DC (s = 0) and infinite frequency (s → ∞), the gain is 1. At the center frequency ω₀, the gain is zero. Band-stop filters are also called notch filters or band-reject filters. The bandwidth is not defined in the same way as for band-pass filters since both low and high frequencies are passed. The quality factor Q determines the sharpness of the notch. A higher Q value results in a narrower notch. An all-pass filter can be designed using a low-pass filter topology. The transfer function is T(s) = (1 - sRC)/(1 + sRC). This form has a zero at s = 1/(RC) and a pole at s = -1/(RC). The phase response is φ(ω) = -2tan⁻¹(ωRC). At ω = 0, φ = 0°. At ω → ∞, φ = -180°. This design uses the low-pass filter topology but produces the same all-pass behavior as the high-pass design. The pole-zero diagram shows a zero at s = 1/(RC) and a pole at s = -1/(RC). The distance between the zero and the origin equals the distance between the pole and the origin, which is a characteristic property of all-pass filters. This configuration makes all-pass filters non-minimum phase systems.

In the s-plane, the notch filter exhibits specific pole-zero placement: zeros lie on the imaginary axis at ±jω₀, while poles are located near the imaginary axis with small negative real parts. At DC (s=0), the numerator and denominator vectors are approximately equal in magnitude, resulting in gain of 1. At high frequencies (s→∞), the highest-order terms dominate and again yield gain of 1. Exactly at the zero frequency (ω=ω₀), the numerator becomes zero regardless of input, producing zero output - confirming the notch behavior.

LTspice is a powerful circuit simulation tool for electronics and electrical engineers. Download from analog.com via Design Resources > Design Tools and Calculators. The interface includes: new schematic button, run button (green arrow), zoom tools, cut/copy/paste, wire tool (pencil), ground symbol, net labeling, component library, move/drag, undo/redo, mirror imaging, text tool for comments, and SPICE directive tool. Keyboard shortcuts: R=resistor, C=capacitor, D=diode, L=inductor, V=voltage source, G/Z=ground, I=current source. Place components using shortcuts or library. Wire components using the wire tool. Set component values by right-clicking (e.g., 10K for resistors, 15V for voltage sources). Run simulation by specifying stop time and start time. View results using the probe tool (pen symbol) to measure node voltages. The error log identifies missing values, helping diagnose issues early.

LTspice is a circuit simulator accessible via personal installation or UIC Virtual Lab remote desktop. For Virtual Lab, type 'desktop uic edu', sign in with UIC credentials, then log into remote desktop. Windows and Mac interfaces differ: Windows uses top menu bar, Mac requires right-clicking the program. To start a new schematic, click the 'New Schematic' icon. Basic components needed are voltage sources, current sources, resistors (2-5), and ground symbol. To place components, click the Component icon, select the component (e.g., Voltage), and click OK. Components snap to grid positions. Multiple copies are created by clicking and dragging. Exit placement mode by pressing Escape or right-clicking. LTspice automatically numbers components with reference designators (V1, V2 for voltage sources, R1, R2 for resistors). To rename, right-click and type the new name. To set values, right-click on the value field and enter the desired value.

This section covers the essential steps for beginning circuit simulation in LTSpice. Users learn to download and install the software, create new schematics, and display the grid for accurate component placement. The tutorial demonstrates adding fundamental components including voltage sources, resistors, operational amplifiers, and ground connections. Key concepts include understanding spice directives like 'liopamp.sub' for ideal op-amps, using the wire tool for circuit connections, and rotating components using the rotate button or Ctrl+R. The section emphasizes that LTSpice wires don't bend automatically and must be manually adjusted.

To create a circuit schematic in LTspice, you need to place basic components including resistors, voltage sources, and ground references. Resistors can be placed by clicking the resistor icon in the toolbar or by pressing the R key. Voltage sources are found in the components menu at the end of the list. Ground symbols provide the reference point for all voltages in the circuit. Components can be connected using the wire tool, which automatically links components without causing short circuits.

LTSpice provides a schematic drawing interface with control icons for zooming, copying, pasting, placing components, connecting with wires, adding grounds, labels, and moving/rotating components. Components are placed via the component button (NAND icon) or F2 key, with options to search for resistors, capacitors, inductors, diodes, and transistors. Components can be rotated with Ctrl+R and mirrored with Ctrl+E. Circuit connections use the wire tool (F3), and every circuit requires a ground symbol (G key). Component values use specific notation: K for kilo (10^3), M for mega (10^6), U for micro (10^-6). Critical: use 'Meg' not 'M' for mega values since 'M' is reserved for milli.

The twin-T network consists of two T-style filters connected in parallel. One branch is an R-C-R low-pass filter that shunts high frequencies to ground, while the other branch is a C-R-C high-pass filter. When configured with specific relationships between component values (R values are equal, and capacitor values are doubled in one leg), these circuits resonate at the same frequency. This creates a notch filter response where the combined circuits produce a deep attenuation at the resonant frequency, typically around 40-50 dB deep, making it effective for removing unwanted frequencies like 60 Hz or 120 Hz interference.

A passive RC low-pass filter is a simple circuit consisting of a resistor and capacitor that allows low-frequency signals to pass through while attenuating high-frequency signals; the filter's cut-off frequency is determined by the formula f_c = 1/(2πRC), where at frequencies below the cut-off point the signal passes unchanged, and above this point the amplitude decreases at a rate of approximately 20 decibels per decade, with the cut-off frequency representing the point where the amplitude is reduced by approximately 30% (or 3 dB).

The Twin-T Oscillator is a low-frequency oscillator circuit that combines two T-networks (one acting as a low-pass filter and the other as a high-pass filter) connected in parallel, where the low-pass filter has resistors in series with a shunt capacitor and the high-pass filter has capacitors in series with a shunt resistor; when both networks are configured with the same cutoff frequency, they form a band-reject filter that enables sustained sinusoidal oscillation at a specific frequency determined by the RC time constant, with the oscillation frequency given by f₀ = 1/(2πRC).

T-filters are fundamental passive filter circuits shaped like the letter T, consisting of three components arranged in specific patterns. The resistor-resistor-capacitor (RRC) configuration functions as a low-pass filter, allowing low frequencies to pass while attenuating high frequencies because capacitors block DC and low-frequency signals but allow high-frequency AC to bypass to ground. Conversely, the capacitor-capacitor-resistor (CCR) configuration acts as a high-pass filter, permitting high frequencies while blocking low frequencies. Both configurations use identical component values (10kΩ resistors and 0.01μF capacitors) and demonstrate complementary frequency response characteristics when tested with an oscilloscope using a logarithmic frequency sweep from 1 Hz to 1 MHz, with the cut-off frequency occurring around 1 kHz for these particular component values.

Passive RC filters are fundamental circuit elements that use resistors and capacitors to create frequency-selective responses; they work by exploiting the frequency-dependent impedance of capacitors (which decreases with increasing frequency) combined with the constant impedance of resistors, enabling the construction of basic filter types including high-pass, low-pass, band-pass, and band-stop configurations, with more advanced designs like twin-T notch filters and limited-attenuation filters offering greater control over frequency response characteristics.