What are resonant frequencies in PCB assembly?

The problem of calculating resonant frequencies is topical in the design of printed circuit assemblies of onboard electronic devices. Analysis of the amplitude-frequency characteristics based on the calculated values of resonant frequencies and their subsequent analysis allows us to draw a conclusion about the technical condition of the object of study.

Changing the Parameters of the Printed Circuit Assembly

Changing the parameters of the printed circuit assembly within the tolerance leads to a spread of resonant frequencies relative to the idealized value, thereby forming admissible intervals of resonant frequencies. The article considers the following methods for calculating the spread of resonant frequencies of a printed circuit assembly: 

• Experimental method
• Worst case method
• Method of moments
• Monte Carlo simulation method

The features of each method were analyzed. After the analysis, the Monte Carlo method seems to have the highest accuracy and ease of implementation, taking into account the computational capabilities of modern electronic computers.

A block diagram of the application of the Monte Carlo method is presented, the mathematical apparatus used is given, and the process of integrating software systems for calculating the spread of resonant frequencies of a printed circuit assembly is described.

Calculation of Resonant Frequencies Spread of Printed Circuit Assembly of Electronic Devices 

The task of calculating the resonant frequencies is relevant in the design of printed circuit assemblies’ structures of onboard electronic devices. Analysis of the amplitude-frequency characteristics based on the estimated values of the resonant frequencies and their subsequent analysis is indicative of the technical condition of the object of study.

All geometrical dimensions of the structural elements of the electronic device and the location of the electronic components on the printed circuit board have to meet the tolerances specified in the design documentation. It is impossible to maintain an exact technology during production; therefore all parameters may have tolerance limits.

Any changes in the parameters of the printed circuit assembly within the tolerance lead to a variation of the resonant frequencies relative to the idealized value, therefore forming the tolerance intervals of the resonant frequencies.

Diversities of the Printed Circuit Resonant Frequencies

The process of integrating software systems for calculating the diversities of the resonant frequencies of a printed circuit assembly is described.

One of the ways to study an electronic device (hereinafter - ES) for the integrity of the structure is through vibration tests as a result of which the amplitude-frequency characteristics are taken for further analysis.

Why vibration control is important in PCB Assembly?

During vibration control, special attention should be paid to the structural elements of the onboard ES, namely, printed circuit assemblies (hereinafter referred to as PU). A structural defect in the PU (crack, detachment of an electric radio element, etc.) can lead to a malfunction of the electrical circuit and, consequently, to the failure of the entire unit.

The analysis of the amplitude-frequency characteristic, as a rule, comes down to comparing the characteristics of a serviceable ES, obtained as a result of simulation, and the tested ES.

The result of applying the Monte Carlo simulation method is the intervals of permissible resonant frequencies of the printed circuit assembly of an electronic device, which can later be used in the analysis of its technical condition.

Calculation of the natural frequency of the printed circuit assembly

The purpose of the practical lesson is to determine the external mechanical overloads acting on the elements of the printed circuit assembly of the RES product, as well as the resulting maximum displacements under the action of vibration and shock.

To assess vibration resistance, it is necessary to calculate the natural (resonant) frequency of the functional unit (FU) board with the electrical radio elements installed on it. The board's natural frequency should not fall within the frequency range at which the device is operated.

 In this case, resonance sets in and the board may fail due to a violation of the integrity of the conductive pattern or the leads of the attachments. Most often, this destabilizing range of external vibrations lies in the range from 1 to 100 Hz.

As a task for calculating the natural frequency of the FU, the design of a functional printed circuit assembly with the appropriate dimensions and weight obtained as a result of designing in the P-CAD system is used. The intended fastening of the printed circuit assembly to the base of the installation object is at 4 points at the corners of the board.

Calculation of the Natural Resonant Frequency of the Printed Circuit Assembly

A functional unit on a rigid printed circuit board, fixed in the device, under vibration loads (for example, when transporting the device by car, aircraft, etc.), has its own frequencies of mechanical vibrations or structural resonances. If the frequency of vibration influences coincides with the natural frequency of the FU, the board experiences maximum mechanical overloads, which can lead to its destruction, the destruction of elements, and the separation of pads, solder contacts, and wires. Mechanical overloads will be minimal if the condition is met:

This condition is the main one when choosing a method for fixing and placing a functional unit in the device. The frequency of vibrations, which is determined by the operating conditions of the device, is usually known, the natural frequency of the node is determined by its mechanical characteristics and is found in the expression:

Another important question arises: why did the parallel resonance of the L ESLCCAVITY circuit with a decoupling capacitor of 1 nF shift to a higher frequency? The natural resonant frequency of the circuit L ESLCDECAP approached a value of 90 MHz.

This is very close to the 100 MHz parallel resonance frequency L ESLCCAVITY of other capacitors. With such a close arrangement to each other, the parallel resonance LESLCCAVITY distorted and shifted slightly higher in frequency. 

This effect can only be seen with a field analyzer

 The simple RLC model and the PDN network approximation do not quite accurately reflect this effect. We emphasize that none of the capacitor values affected the impedance at which the resonances were observed, since they are at very high frequencies, where all the capacitors become open circuits.

Above, we considered the case where the decoupling capacitor was located very close to the U1.1 test point. Now let's see how the removal of the capacitor from this point affects it. It is clear that its location affects only the distributed inductance. If it is small compared to the mounting inductance of the capacitor, its location should not matter.

To answer this question, we will use a 1 uF decoupling capacitor, which we will move to the upper left corner of the board, placing it next to the stabilizer. Leave the dielectric thickness for the hollow resonator at 30 mils. The simulation results characterize the frequency dependence of the impedance of the decoupling capacitor installed in the corner, and the blue characterizes the case of its location in the center.

Conclusion 

So, we have seen how the power supply, decoupling capacitors, and arrays of vias affect the impedance profile of the resonator in different frequency ranges. Parasitic capacitive coupling can occur when a signal passes through vias in a PCB hollow resonator.

This phenomenon is especially critical at high data transfer rates, which is very typical for modern electronic equipment. Due to discrepancies in the shape and size of the layers of the printed circuit board, low-frequency and high-frequency parasitic resonances occur.

Reducing the thickness of the resonator cavity made it possible to reduce its impedance to such an extent that its value was no longer affected by the location of the capacitor. We also saw how important it is for the power distribution network to be transparent to the signal return path.

Click here to learn more about PCB Trace.