群时延的原理Group_delay
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• The upper trace shows magnitude versus frequency: the filter’s bandpass characteristics. The x-axis is frequency, the y-axis is amplitude. • The lower trace shows group delay versus frequency. The x-axis is frequency, the y-axis is time. Note the bathtublike shape of the curve.
Group Delay
© 2005 Cisco Systems, Inc. All rights reserved.
Cisco Public
11
The Analogy
Imagine a group of runners with identical athletic abilities on a smooth, flat track …
Group Delay
© 2005 Cisco Systems, Inc. All rights reserved.
Cisco Public
8
The Formal Definition
Group delay is “the derivative of radian phase with respect to radian frequency. It is equal to the phase delay for an ideal non-dispersive delay device, but may differ greatly in actual devices where there is a ripple in the phase versus frequency characteristic.”
• If propagation or transit time through a device is different at different frequencies, the result is delay shift or non-linear phase shift
If phase changes non-linearly with frequency, the output signal will be distorted
d GD d
where GD is group delay variation, φ is phase in radians, and ω is frequency in radians per second • For the purists, group delay also is defined
Graphic courtesy of Holtzman, Inc.
Group Delay © 2005 Cisco Systems, Inc. All rights reserved.
Cisco Public
6
The Basics
Phase versus frequency
• If propagation or transit time through a device is the same at all frequencies, phase is said to be linear with respect to frequency
IEEE Standard Dictionary of Electrical and Electronics Terms
Group Delay
© 2005 Cisco Systems, Inc. All rights reserved.
Cisco Public
9
The Math (Yikes!)
• In its simplest mathematical representation…
Cisco Public
10
ቤተ መጻሕፍቲ ባይዱ
The Translation (Whew!)
• If phase versus frequency is non-linear, group delay exists. • In a system, network, device or component with no group delay, all frequencies are transmitted through the system, network, device or component in the same amount of time—that is, with equal time delay. • If group delay exists, signals at some frequencies travel faster than signals at other frequencies.
( ) ( )
• And yet another definition is
d d D( ) ( ) H (e j ) d d
Group Delay © 2005 Cisco Systems, Inc. All rights reserved.
The Basics
Bandpass filter equivalent
• Consider the 6 MHz spectrum occupied by an analog TV channel or digitally modulated signal, the 5-42 MHz upstream spectrum, or any specified bandwidth or passband as the equivalent of a bandpass filter.
Group Delay © 2005 Cisco Systems, Inc. All rights reserved.
Cisco Public
7
The Basics
Delay and phase distortion
• Delay distortion—also known as phase distortion— is usually expressed in units of time: milliseconds (ms), microseconds (µs) or nanoseconds (ns) relative to a reference frequency • Phase distortion is related to phase delay • Phase distortion is measured using a parameter called envelope delay distortion, or group delay distortion
Example courtesy of Holtzman, Inc.
Group Delay © 2005 Cisco Systems, Inc. All rights reserved.
All of the athletes arrive at the finish line at exactly the same time and with equal time delay from one end of the track to the other!
Group Delay
© 2005 Cisco Systems, Inc. All rights reserved.
Cisco Public
1
The Basics
Transit time and velocity of propagation
• A signal takes a certain amount of time to pass through a filter
Group Delay
© 2005 Cisco Systems, Inc. All rights reserved.
Cisco Public
2
The Basics
Velocity of propagation versus frequency
• In many instances the velocity of propagation through a filter varies with frequency
Cisco Public
4
The Basics
Delay versus frequency
• If delay through a filter is plotted on a graph of frequency (x-axis) versus time delay (y-axis), the plot often has a parabola- or bathtub-like shape
The transit time through the filter is a function of the filter’s velocity of propagation (also called velocity factor) Velocity of propagation is the speed that an electromagnetic signal travels through some medium, usually expressed as a percentage of the speed of light in a vacuum
© 2005 Cisco Systems, Inc. All rights reserved.
Cisco Public
3
The Basics
Delay and absolute delay
• The finite time required for a signal to pass through a filter—or any device for that matter— is called delay
Time delay
5 4 3 2 1 0
Frequency
Group Delay
© 2005 Cisco Systems, Inc. All rights reserved.
Cisco Public
5
The Basics
Network analyzer plot of Ch. T8 bandpass filter
The velocity of propagation may be greater in the center of the filter’s passband, but slower near the band edges
Passband center
-3 dB point
Group Delay
Absolute delay is the delay a signal experiences passing through the device at some reference frequency
Group Delay
© 2005 Cisco Systems, Inc. All rights reserved.
If phase changes uniformly with frequency, an output signal will be identical to the input signal—except that it will have a time shift because of the uniform delay through the device
Cisco Public
12
Group Delay: An Analogy
Now let’s substitute a group of RF signals for the athletes. Here, the “track” is the equivalent of a filter’s passband.
Group Delay
© 2005 Cisco Systems, Inc. All rights reserved.
Cisco Public
11
The Analogy
Imagine a group of runners with identical athletic abilities on a smooth, flat track …
Group Delay
© 2005 Cisco Systems, Inc. All rights reserved.
Cisco Public
8
The Formal Definition
Group delay is “the derivative of radian phase with respect to radian frequency. It is equal to the phase delay for an ideal non-dispersive delay device, but may differ greatly in actual devices where there is a ripple in the phase versus frequency characteristic.”
• If propagation or transit time through a device is different at different frequencies, the result is delay shift or non-linear phase shift
If phase changes non-linearly with frequency, the output signal will be distorted
d GD d
where GD is group delay variation, φ is phase in radians, and ω is frequency in radians per second • For the purists, group delay also is defined
Graphic courtesy of Holtzman, Inc.
Group Delay © 2005 Cisco Systems, Inc. All rights reserved.
Cisco Public
6
The Basics
Phase versus frequency
• If propagation or transit time through a device is the same at all frequencies, phase is said to be linear with respect to frequency
IEEE Standard Dictionary of Electrical and Electronics Terms
Group Delay
© 2005 Cisco Systems, Inc. All rights reserved.
Cisco Public
9
The Math (Yikes!)
• In its simplest mathematical representation…
Cisco Public
10
ቤተ መጻሕፍቲ ባይዱ
The Translation (Whew!)
• If phase versus frequency is non-linear, group delay exists. • In a system, network, device or component with no group delay, all frequencies are transmitted through the system, network, device or component in the same amount of time—that is, with equal time delay. • If group delay exists, signals at some frequencies travel faster than signals at other frequencies.
( ) ( )
• And yet another definition is
d d D( ) ( ) H (e j ) d d
Group Delay © 2005 Cisco Systems, Inc. All rights reserved.
The Basics
Bandpass filter equivalent
• Consider the 6 MHz spectrum occupied by an analog TV channel or digitally modulated signal, the 5-42 MHz upstream spectrum, or any specified bandwidth or passband as the equivalent of a bandpass filter.
Group Delay © 2005 Cisco Systems, Inc. All rights reserved.
Cisco Public
7
The Basics
Delay and phase distortion
• Delay distortion—also known as phase distortion— is usually expressed in units of time: milliseconds (ms), microseconds (µs) or nanoseconds (ns) relative to a reference frequency • Phase distortion is related to phase delay • Phase distortion is measured using a parameter called envelope delay distortion, or group delay distortion
Example courtesy of Holtzman, Inc.
Group Delay © 2005 Cisco Systems, Inc. All rights reserved.
All of the athletes arrive at the finish line at exactly the same time and with equal time delay from one end of the track to the other!
Group Delay
© 2005 Cisco Systems, Inc. All rights reserved.
Cisco Public
1
The Basics
Transit time and velocity of propagation
• A signal takes a certain amount of time to pass through a filter
Group Delay
© 2005 Cisco Systems, Inc. All rights reserved.
Cisco Public
2
The Basics
Velocity of propagation versus frequency
• In many instances the velocity of propagation through a filter varies with frequency
Cisco Public
4
The Basics
Delay versus frequency
• If delay through a filter is plotted on a graph of frequency (x-axis) versus time delay (y-axis), the plot often has a parabola- or bathtub-like shape
The transit time through the filter is a function of the filter’s velocity of propagation (also called velocity factor) Velocity of propagation is the speed that an electromagnetic signal travels through some medium, usually expressed as a percentage of the speed of light in a vacuum
© 2005 Cisco Systems, Inc. All rights reserved.
Cisco Public
3
The Basics
Delay and absolute delay
• The finite time required for a signal to pass through a filter—or any device for that matter— is called delay
Time delay
5 4 3 2 1 0
Frequency
Group Delay
© 2005 Cisco Systems, Inc. All rights reserved.
Cisco Public
5
The Basics
Network analyzer plot of Ch. T8 bandpass filter
The velocity of propagation may be greater in the center of the filter’s passband, but slower near the band edges
Passband center
-3 dB point
Group Delay
Absolute delay is the delay a signal experiences passing through the device at some reference frequency
Group Delay
© 2005 Cisco Systems, Inc. All rights reserved.
If phase changes uniformly with frequency, an output signal will be identical to the input signal—except that it will have a time shift because of the uniform delay through the device
Cisco Public
12
Group Delay: An Analogy
Now let’s substitute a group of RF signals for the athletes. Here, the “track” is the equivalent of a filter’s passband.