What are Bode plots?
How to use Bode plots for high pass filter design.
How to incorporate Bode plot high pass filter parameters into board design.
The 5G transmission speed transformation
Over the years, especially the last half-century or so, there have been a number of exciting eras in which technology took a giant step forward. However, today has to rank near the top of these. With the use of AI-enabling real-time adaptation, IoT providing connectivity between machines within and between factories, and Industry 4.0 transforming industrial production, these are fascinating times indeed! The common thread that enables all of these technological advancements is the constant improvement in communications, which is undergoing its own transformation through the implementation of 5G system designs.
An essential requirement for high-speed communication circuit boards is filtering. There are many filter design methods and techniques available. Primarily, these are used to determine the best components that will provide the highest fidelity of the pass band(s). Some of these methods are quite involved and require complex circuit analysis to utilize, which are often necessary for custom filter designs. A much simpler alternative that is quite effective and can be used to choose appropriate IC modules or in conjunction with simple high pass filter passive component selection is the Bode plot.
Let’s take a look at Bode plot high pass filter design and how the parameters derived can be used to aid in designing your PCBA.
What are Bode Plots and How Are They Used?
Bell Labs engineer, Hendrik Wade Bode (who also spent some time as a professor at Harvard), came up with the Bode plot, which can be defined as follows:
Bode plots are idealized graphs that are used to design filters and amplifiers for bandpass, band reject, low pass, and high pass frequency requirements. How to use a Bode plot high pass filter design is discussed in the next section.
Designing High Pass Filters with Bode Plots
An example of a high pass Bode magnitude plot is shown in the figure below.
Fig. 1 Bode magnitude plot for high pass filter
As shown in Figure 1, the magnitude frequency response is divided into two sections: the Stop band, where signals are blocked, and the Pass band, above which all signals are allowed to pass through. The dividing line for the two sections is the cutoff frequency, fC. From fC to the 0 dB line is the transition interval during which there is a fixed slope of 20dB/decade for passive filters. In Figure 2, the phase response is shown.
Fig. 2 Bode phase plot for high pass filter
As shown above, during the Passband, there is no phase shift through the system and the output is in phase with the input. In equation form, the input, output and system are related as follows:
Vout(j⍵) = Vin(j⍵) x H(j⍵) (1)
where H(j⍵) = 1/(1+j(⍵C/⍵)) is the system transfer function.
The gain for the filter is shown in Eq. (2).
Av = 20log(Vout/Vin) (2)
Bode plot high pass filter designs can be used for passive filters and active filters, which are often referred to as amplifiers since their gain can be greater than unity which is not possible for passive designs. For passive filters, there are basically two types: RC and RL. The resistive, capacitive, and inductive components are selected to achieve the desired cutoff frequency using Eq. (3) or (4).
fC = 1/(2𝛑RC) (3)
fC = R/(2𝛑L) (4)
For active filters, the design is more complicated and depends on the filter design type (e.g. Butterworth, Chebyshev, etc.) and the order, which is generally used to steepen the transition angle. Now, let’s see how Bode plots can help with board design.
PCBA Design Based on Bode Plot High Pass Filter Parameters
For the best board design, you need to know the range of signals for inputs and/or outputs and components, as well. Moreover, to achieve the maximum power transfer for these signals, you need to know trace impedances. These impedances are determinable from the copper weights and lengths selected for your transmission lines. Therefore, knowing the resistance of components, modules, and external loads can assist you in determining the best trace parameters.
For high-frequency boards, maintaining a constant impedance over the passband is important for power integrity and signal integrity. Not only is impedance important on the board surface, but also for creating the best PCB layer stackup. The most often-used technique is either fixed impedance and a constant dielectric constant for the layers, as shown in the figure below.
Stackup design using fixed dielectric constant
With Cadence’s PCB Design and Analysis package, the Bode plot high pass filter parameters, coupled with the simulation and analysis capabilities of Allegro PCB Editor, can be utilized to improve schematic optimization, PCBA layout, and design manufacturability.
If you’re looking to learn more about how Cadence has the solution for you, talk to us and our team of experts.