• Latest
  • Trending
  • All
  • Capacitors
  • Resistors
  • Inductors
  • Filters
  • Fuses
  • Non-linear Passives
  • Applications
  • Integrated Passives
  • Oscillators
  • Passive Sensors
  • New Technologies
  • Aerospace & Defence
  • Automotive
  • Industrial
  • Market & Supply Chain
  • Medical
  • RF & Microwave
  • Telecommunication

Filter Q Factor Explained

4.1.2023

Exploring the Benefits of High-Performance MLCC Capacitors for Aerospace and Defense

23.3.2023

Murata Establishes Joint Venture Company to Produce MLCC Raw Materials

23.3.2023

Examining the Influence of ESR and Ripple Current on Selecting the Suitable Capacitor

21.3.2023

SABIC Validates its 150°C Film Foil to Enable Adoption of Film Capacitors in SIC Power Modules

20.3.2023

Outlook of Passive Electronic Components Market for Oil & Gas Electronics in 2023

20.3.2023

Flying Capacitors Explained

17.3.2023
  • Home
  • Privacy Policy
  • EPCI Membership & Advertisement
  • About
No Result
View All Result
NEWSLETTER
Passive Components Blog
  • Home
  • NewsFilter
    • All
    • Aerospace & Defence
    • Antenna
    • Applications
    • Automotive
    • Capacitors
    • Circuit Protection Devices
    • Filters
    • Fuses
    • Inductors
    • Industrial
    • Integrated Passives
    • Market & Supply Chain
    • Medical
    • New Materials & Supply
    • New Technologies
    • Non-linear Passives
    • Oscillators
    • Passive Sensors
    • Resistors
    • RF & Microwave
    • Telecommunication

    Exploring the Benefits of High-Performance MLCC Capacitors for Aerospace and Defense

    Murata Establishes Joint Venture Company to Produce MLCC Raw Materials

    Examining the Influence of ESR and Ripple Current on Selecting the Suitable Capacitor

    SABIC Validates its 150°C Film Foil to Enable Adoption of Film Capacitors in SIC Power Modules

    Outlook of Passive Electronic Components Market for Oil & Gas Electronics in 2023

    Flying Capacitors Explained

    TDK Introduces Compact High-Current Chokes for Automotive and Industrial Applications

    ECIA NA February 2023 Electronic Components Sales Confirms Growth Trend

    Investigating Modeling Techniques of Class II Ceramic Capacitors Losses for High Voltage and Current Applications

    Trending Tags

    • Ripple Current
    • RF
    • Leakage Current
    • Tantalum vs Ceramic
    • Snubber
    • Low ESR
    • Feedthrough
    • Derating
    • Dielectric Constant
    • New Products
    • Market Reports
  • VideoFilter
    • All
    • Antenna videos
    • Capacitor videos
    • Filter videos
    • Fuse videos
    • Inductor videos
    • Non-linear passives videos
    • Oscillator videos
    • Passive sensors videos
    • Resistor videos
    • Sensors

    Investigating Modeling Techniques of Class II Ceramic Capacitors Losses for High Voltage and Current Applications

    Understanding Basics of Current Sense Resistors

    What Decoupling Capacitor Value To Use And Where To Place Them

    How to Measure Rated Current on Power Inductors

    LTspice Simulation of a Spark-Gap Circuit Protection Surge Arrester

    Approximate Inductor Design Using Two Alternative Cores

    1kW Phase Shift Full Bridge Converter Design and Simulation

    Multiphase Buck Trans-Inductor Voltage Regulator (TLVR) Explained

    Smart Power Distribution Unit Architecture and Inductor Losses

    Trending Tags

    • Capacitors explained
    • Inductors explained
    • Resistors explained
    • Filters explained
    • Application Video Guidelines
    • EMC
    • New Products
    • Ripple Current
    • Simulation
    • Tantalum vs Ceramic
  • Knowledge Blog
  • Suppliers
    • Preferred Suppliers
    • Who is Who
  • Events
  • Home
  • NewsFilter
    • All
    • Aerospace & Defence
    • Antenna
    • Applications
    • Automotive
    • Capacitors
    • Circuit Protection Devices
    • Filters
    • Fuses
    • Inductors
    • Industrial
    • Integrated Passives
    • Market & Supply Chain
    • Medical
    • New Materials & Supply
    • New Technologies
    • Non-linear Passives
    • Oscillators
    • Passive Sensors
    • Resistors
    • RF & Microwave
    • Telecommunication

    Exploring the Benefits of High-Performance MLCC Capacitors for Aerospace and Defense

    Murata Establishes Joint Venture Company to Produce MLCC Raw Materials

    Examining the Influence of ESR and Ripple Current on Selecting the Suitable Capacitor

    SABIC Validates its 150°C Film Foil to Enable Adoption of Film Capacitors in SIC Power Modules

    Outlook of Passive Electronic Components Market for Oil & Gas Electronics in 2023

    Flying Capacitors Explained

    TDK Introduces Compact High-Current Chokes for Automotive and Industrial Applications

    ECIA NA February 2023 Electronic Components Sales Confirms Growth Trend

    Investigating Modeling Techniques of Class II Ceramic Capacitors Losses for High Voltage and Current Applications

    Trending Tags

    • Ripple Current
    • RF
    • Leakage Current
    • Tantalum vs Ceramic
    • Snubber
    • Low ESR
    • Feedthrough
    • Derating
    • Dielectric Constant
    • New Products
    • Market Reports
  • VideoFilter
    • All
    • Antenna videos
    • Capacitor videos
    • Filter videos
    • Fuse videos
    • Inductor videos
    • Non-linear passives videos
    • Oscillator videos
    • Passive sensors videos
    • Resistor videos
    • Sensors

    Investigating Modeling Techniques of Class II Ceramic Capacitors Losses for High Voltage and Current Applications

    Understanding Basics of Current Sense Resistors

    What Decoupling Capacitor Value To Use And Where To Place Them

    How to Measure Rated Current on Power Inductors

    LTspice Simulation of a Spark-Gap Circuit Protection Surge Arrester

    Approximate Inductor Design Using Two Alternative Cores

    1kW Phase Shift Full Bridge Converter Design and Simulation

    Multiphase Buck Trans-Inductor Voltage Regulator (TLVR) Explained

    Smart Power Distribution Unit Architecture and Inductor Losses

    Trending Tags

    • Capacitors explained
    • Inductors explained
    • Resistors explained
    • Filters explained
    • Application Video Guidelines
    • EMC
    • New Products
    • Ripple Current
    • Simulation
    • Tantalum vs Ceramic
  • Knowledge Blog
  • Suppliers
    • Preferred Suppliers
    • Who is Who
  • Events
No Result
View All Result
Passive Components Blog
No Result
View All Result

Filter Q Factor Explained

4.1.2023
Reading Time: 10 mins read
0 0
0
SHARES
3k
VIEWS

This blog article from Knowles Precision Devices perform a deep dive on the different ways you can think about Q factor for the components going into filter or filter as a whole. 

As an RF engineer, you likely frequently hear the term “quality factor”, or Q factor, used as shorthand figure of merit (FOM) for RF filters.

RelatedPosts

Exploring the Benefits of High-Performance MLCC Capacitors for Aerospace and Defense

Flying Capacitors Explained

Filter Shape Factor and Selectivity

In short, Q factor is expressed as the ratio of stored versus lost energy per oscillation cycle.

 More specifically, Q factor generally describes specifications such as the steepness of skirts, or the selectivity, and how low the insertion loss is. Overall losses through a resonator increase as Q factor drops and will increase more rapidly with frequency for lower values of resonator Q.

However, truly understanding how Q factor is determined is a bit more intricate. Let’s start by looking back to the example bandpass filter specification we showed in this article.

Figure 1. An example of a typical bandpass filter response.

In this example, the X axis shows the operating frequency of the bandpass filter while the Y axis shows the power allowed through the filter in decibels. We can mark the following characteristics of this filter on this graph: 

  • Center frequency – The geometric or arithmetic mean of the upper and lower cutoff frequencies or 3dB points of the bandpass filter.
  • Bandwidth – Usually taken from the 3dB points on either side of the center frequency.
  • Insertion loss – Drawn here as the loss at the center frequency. In general, when someone says high Q in reference to insertion loss, this usually means low insertion loss.
  • Selectivity – This is a measurement of a filter’s ability to pass or reject specific frequencies closer to the band of interest. This is what people usually mean when they talk about ‘steep skirts’ or a ‘sharp response.’ Generally, high Q means high selectivity.

Understanding the Different Components of Q Factor

There are three types of Q – loaded (QL), unloaded Q (Qu), and external Q (Qe) that make up Q factor. QL is measured by looking at a plot of a filter’s performance. The standard definition of QL is as a FOM for bandwidth calculated with the following equation:

QL is driven by what goes on inside the filter, which is the Qu, and the way that the device is coupled to the external world, which is the Qe:

In general, QL is a convenient way to talk about a filter’s performance as plotted. But when it comes to what makes a filter work the way it does, it’s best to look at the QU of the resonators the filter is built up from. Now let’s look more specifically at three different ways to define Q factor using the different types of Q.

Three Ways to Define Q Factor

As mentioned, there are actually a few different ways to define Q factor, depending on the context of the discussion. This includes the following:

  • Bandpass Q Factor – This talks about the width of a filter. Sometimes this is QL ,as discussed above, but with wide filters it is tricky to use Bandpass Q Factor
  • Component Q Factor – Addresses individual inductor or capacitor Q
  • Pole Q Factor – Tells us about the performance of different parts of a filter response, and is more abstract and based on Pole Zero Plots

While component and bandpass Q are the two most common types of Q factor referenced, let’s further explore the context of all three to better understand what someone may mean when they say a filter or component has “high Q.”

Bandpass Q Factor

When connecting components to create a resonant circuit, we need to look at QL, which for bandpass filters is referring to selectivity as shown in Figure 2.

Figure 2. A graph showing bandpass filter Q Factor.

If the resonant circuit has Bandpass properties, we can define QL with the following formula:

It is important to note that this approach works for narrowband filters. However, when f1 and f2 are widely separated, which usually means two octaves or more between f1 and f2, this results in a wideband with the filter often constructed by combining a high pass filter for f1 and a low pass filter for f2. In this situation it might make sense to think about the pole quality factor instead, which we will discuss later in this post, or to look at the performance of the high pass and low pass sections and look at their QL. 

Component Q Factor

As mentioned, component Q factor looks at just the component, such as the inductor or capacitor, in isolation from the rest of the circuit. Components have Qu related to the component values and loss. Since inductance and capacitance provide an opposition to AC that is measured in terms of reactance, let’s look at Q in terms of how the component behaves under reactance.

For a reactance with no loss: 

For an Inductive reactance, Q increases with frequency and decreases with loss:

For capacitive reactance, Q decreases with frequency and with loss:

More specifically, the Q of an individual reactive component depends on the frequency at which it is evaluated, which is typically the resonant frequency of the circuit that it is used in. The formula for Q depends on whether we imagine the R to be in series with or in parallel with the reactance. The following formulas can be used to calculate Qu: 

Pole Q Factor

For more complex system such as wider filters, we can look at the pole Q factor, which tells us about the performance of different parts of the filter response. A filter has a transfer function H(s) which tells us what an output signal will look like for a given input signal.

Filter Transfer Functions are expressed in terms of the complex variable ‘s’ because some problems are much easier so solve in the Laplace domain than they are in the time domain. The output signal Y(s) can be converted back into real numbers, and we can see how a filter’s performance is determined by the structure of the transfer function H(s). We can find the values for s for when the transfer function either gets large because the denominator heads to zero, or gets small because the numerator heads to zero.

When heads to zero we call these values of s ‘zeros’ because the transfer function tends to get smaller. When heads to zero we call these values of s “poles” because the transfer function tends to get larger. In the Pole Zero Plot in Figure 3, you can see that the poles are marked with an X.

Figure 3. A Pole Zero Plot that shows Pole Q factor.

In this plot there are two poles that are complex conjugate pairs. The length of the arrow from the origin to the X is the frequency ωp. The distance along the real axis can be written in terms of the Q factor: 

Poles and zeros come from analyzing the system as a whole. Poles close to the y axis enhance amplitude response, making that part of the filter “sharp,” which is one of the ways Q factor drives selectivity. Additionally, based on this plot, high Q for a pole means low sigma. Since earlier we said this real component has to do with damping, which in turn is related to energy loss of a resonator, this makes sense. 

Source: Knowles Precision Devices

Related Posts

Capacitors

Examining the Influence of ESR and Ripple Current on Selecting the Suitable Capacitor

21.3.2023
84
Capacitors

Flying Capacitors Explained

17.3.2023
50
Capacitors

Investigating Modeling Techniques of Class II Ceramic Capacitors Losses for High Voltage and Current Applications

15.3.2023
102

Upcoming Events

Mar 19
March 19 - March 23

APEC 2023

Apr 3
April 3 @ 12:00 - April 4 @ 14:00 CEST

Microelectronic Packaging Failure Modes and Analysis

Apr 5
11:00 - 12:00 CEST

Plugging – Filling – Tenting; WE PCB Webinar

View Calendar

Popular Posts

  • Ripple Current and its Effects on the Performance of Capacitors

    3 shares
    Share 3 Tweet 0
  • What is a Dielectric Constant of Plastic Materials ?

    4 shares
    Share 4 Tweet 0
  • Capacitor Selection for Coupling and Decoupling Applications

    28 shares
    Share 28 Tweet 0
  • How to Choose the Right Inductor for DC-DC Buck Applications

    0 shares
    Share 0 Tweet 0
  • Leakage Current Characteristics of Capacitors

    0 shares
    Share 0 Tweet 0
  • Understanding High-Precision Resistor Temperature Coefficient of Resistance

    0 shares
    Share 0 Tweet 0
  • Why Low ESR Matters in Capacitor Design

    0 shares
    Share 0 Tweet 0
  • MLCC and Ceramic Capacitors

    0 shares
    Share 0 Tweet 0

Newsletter Subscription

 

PCNS Call for Papers !

Archive

2022
2021
2020
2019
2018
2017

Symposium

Passive Components Networking Symposium

Passives e-Learning

Knowledge Blog

  • Home
  • Privacy Policy
  • EPCI Membership & Advertisement
  • About

© EPCI - Premium Passive Components Educational and Information Site

No Result
View All Result
  • Home
  • News
  • Video
  • Knowledge Blog
  • Preferred Suppliers
  • Events

© EPCI - Premium Passive Components Educational and Information Site

Welcome Back!

Login to your account below

Forgotten Password?

Retrieve your password

Please enter your username or email address to reset your password.

Log In
This website uses cookies. By continuing to use this website you are giving consent to cookies being used. Visit our Privacy and Cookie Policy.