Which capacitors deal with corner frequency

Capacitors play a pivotal role in electronic circuits influencing various parameters including the corner frequency which is crucial in filter design. This article aims to explore the intricacies of capacitors concerning corner frequency focusing on their types suitable for decoupling understanding filter corner frequency methods to find corner frequency and the impact of capacitor types on the low-frequency region.

I. Introduction to Capacitors and Corner Frequency

A capacitor is formed when two metallic conductors are separated by an insulating material.

The schematic diagram of a parallel plate capacitor is shown in Figure (a).

The metal plates separated by insulating material are called electrodes, which can be connected to the circuit through wires. The insulating material separating the plates is called the dielectric. The commonly used symbol for capacitors in circuits is shown in Figure (b).

When the capacitor's electrodes are connected to a power source, due to the electric field force, positive charges will appear on the electrode connected to the positive terminal of the power source, and negative charges will appear on the electrode connected to the negative terminal, as shown in Figure (c).

The amount of charge on both electrodes is equal, establishing an electric field in the dielectric of the plates, thus storing a certain amount of electric field energy in the capacitor.

What Type of Capacitor to Use for Decoupling?

Definition and purpose of decoupling capacitors:

Decoupling capacitors mainly serve two purposes:

1. Remove high-frequency signal interference.

2. Energy storage (nearby capacitors in chips also serve an energy storage role, which is secondary).

When high-frequency devices operate, their current is discontinuous and at high frequencies. Even if the distance between the device's VCC and the main power supply is short, the impedance \( Z = i \cdot wL + R \) can be significantly affected by the inductance of the line, causing the device to not receive the current it needs promptly.

Decoupling capacitors can compensate for this shortcoming, which is why many circuit boards place small capacitors near the VCC pins of high-frequency devices (typically, a decoupling capacitor is connected in parallel at the VCC pin to ground the AC component).

Types of capacitors best suited for decoupling applications:

- 4.7μF tantalum capacitors are effective at filtering low-frequency noise.

- 0.1μF, 0603 ceramic capacitors are more effective than tantalum capacitors at filtering noise in the 1-50MHz range.

- 0.001μF, 0402 ceramic capacitors are effective at filtering high-frequency noise above 50MHz.

The specific noise frequency band can be determined through circuit analysis (clock frequency) and measurements, which will dictate the type and package of the capacitor used for decoupling. In most cases, using a 0.1μF ceramic capacitor in conjunction with a tantalum capacitor is sufficient to meet system requirements for power noise decoupling.

Electrolytic capacitors: when to use them for low-frequency decoupling:

Low-frequency noise decoupling usually requires electrolytic capacitors (typically ranging from 1μF to 100μF) to serve as a charge reservoir for low-frequency transient currents.

Connecting low-inductance surface-mount ceramic capacitors (typically 0.01μF to 0.1μF) directly to IC power pins can maximally suppress high-frequency power noise. All decoupling capacitors must be connected directly to a low-inductance ground plane to be effective. This connection requires short traces or vias to minimize additional series inductance.

Most IC datasheets provide recommended power decoupling circuits in the application section, and users should always follow these recommendations to ensure proper device operation.

Ferrite beads (insulating ceramics made from oxides or other compounds of nickel, zinc, and manganese) can also be used for decoupling in power filters. Ferrites are inductive at low frequencies (<100kHz) and thus useful for low-pass LC decoupling filters. Above 100kHz, ferrites become resistive (low Q). Ferrite impedance is a function of material, operating frequency range, DC bias current, number of turns, size, shape, and temperature.

Ferrite beads are not always necessary but can enhance high-frequency noise isolation and decoupling, typically providing advantages. It is important to ensure that ferrite beads never saturate, especially when operational amplifiers drive high output currents.

When ferrites saturate, they become nonlinear and lose their filtering properties. Some ferrites may even become nonlinear before fully saturating. Therefore, if a power stage operates near this saturation region, the ferrite should be checked during prototyping.

Factors influencing the choice of decoupling capacitors:

Due to the frequency characteristics of capacitors and device layout on the PCB, the noise suppression effect is also influenced. The non-ideal case distributed parameter equivalent circuit of capacitors is shown below:

- C represents the nominal capacitance.

- RS is the equivalent series resistance (ESR).

- L represents the equivalent series inductance (ESL).

- RP represents the insulation resistance and leakage current, which can be ignored in decoupling applications.

- RDA and CDA represent the dielectric absorption (DA) loss parameters, which can also be ignored in decoupling applications.

In summary, the key parameters affecting the decoupling capacitor are C, ESR, and ESL.

What is the Filter Corner Frequency?

Explanation of filter corner frequency and its importance in filter design:

A filter is a circuit that allows certain frequencies to pass while blocking others. There are four main types of filters: low-pass filters, high-pass filters, band-pass filters, and band-stop (or notch) filters.

- Low-pass filters allow only the low-frequency components of the input signal to pass through.

- High-pass filters allow only the high-frequency components of the signal to pass.

- Band-pass filters allow only a narrow band of frequencies around the filter's resonance frequency to pass.

- Notch filters allow all frequencies except a narrow band centered around the filter's resonance frequency to pass.

Filters are used to process signals to obtain better signal quality. Filters can suppress noise in signals, improve signal-to-noise ratio, suppress oscillations in signals, improve stability, and suppress interference, improving signal reliability. Understanding the role of filters can help you better utilize analog electronics to improve signal quality.

Filters act as frequency-selective devices, allowing specific frequency components of the signal to pass while significantly attenuating others. By using this frequency-selective characteristic, interference noise can be filtered out, or spectral analysis can be performed.

The role of a filter is to allow useful signals to pass through with minimal attenuation while reflecting unwanted signals as much as possible. Filters typically have two ports: an input signal and an output signal, utilizing this characteristic to select a square wave group or composite noise wave passing through the filter to obtain a sine wave of a specific frequency.

The filter's function is to allow signals of certain frequencies to pass smoothly while significantly suppressing signals of other frequencies. Essentially, it is a frequency-selective circuit.

In filters, the frequency range that signals can pass through is called the passband, while the frequency range where signals are significantly attenuated or completely suppressed is called the stopband. The boundary frequency between the passband and the stopband is called the cutoff frequency.

Relationship between capacitors and the corner frequency of filters:

Filter capacitors are connected in parallel at the output of the rectified power circuit to reduce the AC ripple factor and smooth the DC output. In electronic circuits that convert AC to DC, filter capacitors not only stabilize the DC output but also reduce the alternating ripple impact on the electronic circuit, absorbing current fluctuations generated during the operation of the electronic circuit and interference introduced through the AC power supply, thus stabilizing the performance of the electronic circuit.

How to Find Corner Frequency?

Mathematical formulae for calculating corner frequency:

The angular velocity \( \omega \) in the formula \( e = E_m \sin \omega t \) is often referred to as angular frequency or angular speed. It represents the electrical angle through which AC changes per second, i.e., \( \omega = \alpha/t \). Here, the electrical angle is usually expressed in radians, so the unit of \( \omega \) is radians/second.

Within one period \( T \), the angle rotated by the generator coil is \( 2\pi \) (radians), thus the relationship is:

\[ \omega = \frac{2\pi}{T} = 2\pi f \]

Step-by-step guide to determining corner frequency in practical scenarios:

The frequency calculation method is as follows:

1. Basic concept: In the complex plane, an angle can be represented by the angular angle or magnitude angle. Within the range of 0 to 2π, the angular and magnitude angles are the same. In electrical engineering, the magnitude angle is often used to represent angular frequency.

2. Relationship: The relationship between angular frequency \( \omega \) and magnitude angle \( \theta \) is: equal to \( d\theta/dt \), meaning angular frequency is the rate of change of the magnitude angle with time. When the frequency of a sine or cosine wave increases, the corresponding angle (or phase) also increases and changes faster.

3. Maximum leading angle: If we have a sine wave whose phase leads by a certain angle, this angle is called the leading angle. The maximum leading angle corresponds to the maximum frequency or angular frequency.

4. Calculation method: To find the frequency corresponding to the maximum leading angle, we first need to know the position of this angle in the complex plane. Then, use the above relationship to calculate the corresponding angular frequency.

5. Considerations: In practical applications