print | close
`
`Back to Basics: Impedance Matching (Part 1)
`
`Electronic Design
`Lou Frenzel
`Louis E. Frenzel
`Mon, 20111024 15:46
`
`The term “impedance matching” is rather straightforward. It’s simply defined as the process of making one
`impedance look like another. Frequently, it becomes necessary to match a load impedance to the source or
`internal impedance of a driving source.
`
`A wide variety of components and circuits can be used for impedance matching. This series summarizes the
`most common impedancematching techniques.
`
`Rationale And Concept
`
`The maximum powertransfer theorem says that to transfer the maximum amount of power from a source
`to a load, the load impedance should match the source impedance. In the basic circuit, a source may be dc or
`ac, and its internal resistance (Ri) or generator output impedance (Zg) drives a load resistance (RL) or
`impedance (ZL) (Fig. 1):
`
`RL = Ri or ZL = Zg
`
`Fig 1. Maximum power is transferred from a source to a load when the load resistance equals the internal
`resistance of the source.
`
`Page 1 of 10
`
`ADVANCED ENERGY INDUSTRIES INC.
`Exhibit 1009
`
`
`
`Back to Basics: Impedance Matching (Part 1)
`
`Electronic Design
`Lou Frenzel
`Louis E. Frenzel
`Mon, 20111024 15:46
`
`The term “impedance matching” is rather straightforward. It’s simply defined as the process of making one
`impedance look like another. Frequently, it becomes necessary to match a load impedance to the source or
`internal impedance of a driving source.
`
`A wide variety of components and circuits can be used for impedance matching. This series summarizes the
`most common impedancematching techniques.
`
`Rationale And Concept
`
`The maximum powertransfer theorem says that to transfer the maximum amount of power from a source
`to a load, the load impedance should match the source impedance. In the basic circuit, a source may be dc or
`ac, and its internal resistance (Ri) or generator output impedance (Zg) drives a load resistance (RL) or
`impedance (ZL) (Fig. 1):
`
`RL = Ri or ZL = Zg
`
`Fig 1. Maximum power is transferred from a source to a load when the load resistance equals the internal
`resistance of the source.
`
`Page 1 of 10
`
`ADVANCED ENERGY INDUSTRIES INC.
`Exhibit 1009
`
`
`
`Related
`
`Back to Basics: Impedance Matching (Part 2)
`
`Back to Basics: Impedance Matching (Part 3)
`
`Welcome To Antennas 101
`
`Back To Amp Camp
`
`A plot of load power versus load resistance reveals that matching load and source impedances will achieve
`maximum power (Fig. 2).
`
`Fig 2. Varying the load resistance on a source shows that maximum power to the load is achieved by
`matching load and source impedances. At this time, efficiency is 50 %.
`
`A key factor of this theorem is that when the load matches the source, the amount of power delivered to the
`load is the same as the power dissipated in the source. Therefore, transfer of maximum power is only 50%
`efficient.
`
`The source must be able to dissipate this power. To deliver maximum power to the load, the generator has
`to develop twice the desired output power.
`
`Applications
`
`Delivery of maximum power from a source to a load occurs frequently in electronic design. One example is
`when the speaker in an audio system receives a signal from a power amplifier (Fig. 3). Maximum power is
`delivered when the speaker impedance matches the output impedance of the power amplifier. While this is
`theoretically correct, it turns out that the best arrangement is for the power amplifier impedance to be less
`than the speaker impedance. The reason for this is the complex nature of the speaker as a load and its
`
`Page 2 of 10
`
`ADVANCED ENERGY INDUSTRIES INC.
`Exhibit 1009
`
`
`
`mechanical response.
`
`Fig 3. Unmatched impedances provide the best amplifier and speaker performance.
`
`Another example involves power transfer from one stage to another in a transmitter (Fig. 4). The complex
`(R ± jX) input impedance of amplifier B should be matched to the complex output impedance of amplifier A.
`It’s crucial that the reactive components cancel each other. One other example is the delivery of maximum
`power to an antenna (Fig. 5). Here, the antenna impedance matches the transmitter output impedance.
`
`Fig 4. Impedances in radiofrequency transmitters must be matched to pass maximum power from stage
`
`Page 3 of 10
`
`ADVANCED ENERGY INDUSTRIES INC.
`Exhibit 1009
`
`
`
`to stage. Most impedances include inductances and capacitances that must also be factored into the
`matching process.
`
`Fig 5. Antenna impedance must equal the transmitter output impedance to receive maximum power.
`
`TransmissionLine Matching
`
`This last example emphasizes another reason why impedance matching is essential. The transmitter output
`is usually connected to the antenna via a transmission line, which is typically coax cable. In other
`applications, the transmission line may be a twisted pair or some other medium.
`
`A cable becomes a transmission line when it has a length greater than λ/8 at the operating frequency where:
`
`For example, the wavelength of a 433MHz frequency is:
`
`λ = 300/fMHz
`
`λ = 300/fMHz = 300/433 = 0.7 meters or 27.5 inches
`
`A connecting cable is a transmission line if it’s longer than 0.7/8 = 0.0875 meters or 3.44 inches. All
`transmission lines have a characteristic impedance (ZO) that’s a function of the line’s inductance and
`capacitance:
`
`ZO = √(L/C)
`
`Page 4 of 10
`
`ADVANCED ENERGY INDUSTRIES INC.
`Exhibit 1009
`
`
`
`To achieve maximum power transfer over a transmission line, the line impedance must also match the
`source and load impedances (Fig. 6). If the impedances aren’t matched, maximum power will not be
`delivered. In addition, standing waves will develop along the line. This means the load doesn’t absorb all of
`the power sent down the line.
`
`Fig 6. Transmission lines have a characteristic impedance (Z O) that must match the load to ensure
`maximum power transfer and withstand loss to standing waves.
`
`Consequently, some of that power is reflected back toward the source and is effectively lost. The reflected
`power could even damage the source. Standing waves are the distributed patterns of voltage and current
`along the line. Voltage and current are constant for a matched line, but vary considerably if impedances do
`not match.
`
`The amount of power lost due to reflection is a function of the reflection coefficient (Γ) and the standing
`wave ratio (SWR). These are determined by the amount of mismatch between the source and load
`impedances.
`
`The SWR is a function of the load (ZL) and line (ZO) impedances:
`
`SWR = ZL/ZO (for ZL > ZO)
`
`SWR = ZO/ZL (for ZO > ZL)
`
`For a perfect match, SWR = 1. Assume ZL = 75 Ω and ZO = 50 Ω:
`
`SWR = ZL/ZO = 75/50 = 1.5
`
`The reflection coefficient is another measure of the proper match:
`
`Γ = (ZL – ZO)/(ZL + ZO)
`
`For a perfect match, Γ will be 0. You can also compute Γ from the SWR value:
`
`Γ = (SWR – 1)/(SWR + 1)
`
`Calculating the above example:
`
`Page 5 of 10
`
`ADVANCED ENERGY INDUSTRIES INC.
`Exhibit 1009
`
`
`
`Γ = (SWR – 1)/(SWR + 1) = (1.5 – 1)/(1.5 + 1) = 0.5/2.5 = 0.2
`
`Looking at amount of power reflected for given values of SWR (Fig. 7), it should be noted that an SWR of 2
`or less is adequate for many applications. An SWR of 2 means that reflected power is 10%. Therefore, 90%
`of the power will reach the load.
`
`Fig 7. This plot illustrates reflected power in an unmatched transmission line with respect to SWR.
`
`Keep in mind that all transmission lines like coax cable do introduce a loss of decibels per foot. That loss
`must be factored into any calculation of power reaching the load. Coax datasheets provide those values for
`various frequencies.
`
`Another important point to remember is that if the line impedance and load are matched, line length doesn’t
`matter. However, if the line impedance and load don’t match, the generator will see a complex impedance
`that’s a function of the line length.
`
`Reflected power is commonly expressed as return loss (RL). It’s calculated with the expression:
`
`PIN represents the input power to the line and PREF is the reflected power. The greater the dB value, the
`
`RL (in dB) = 10log (PIN/PREF)
`
`Page 6 of 10
`
`ADVANCED ENERGY INDUSTRIES INC.
`Exhibit 1009
`
`
`
`smaller the reflected power and the greater the amount of power delivered to the load.
`
`Impedance Matching
`
`The common problem of mismatched load and source impedances can be corrected by connecting an
`impedancematching device between source and load (Fig. 8). The impedance (Z) matching device may be
`a component, circuit, or piece of equipment.
`
`Fig 8. An impedancematching circuit or component makes the load match the generator impedance.
`
`A wide range of solutions is possible in this scenario. Two of the simplest involve the transformer and the
`λ/4 matching section. A transformer makes one impedance look like another by using the turns ratio
`(Fig. 9):
`
`N = Ns/Np = turns ratio
`
`Fig 9. A transformer offers a near ideal method for making one impedance look like another.
`
`N is the turns ratio, Ns is the number of turns on the transformer’s secondary winding, and Np is the
`number of turns on the transformer’s primary winding. N is often written as the turns ratio Ns:Ns.
`
`The relationship to the impedances can be calculated as:
`
`Page 7 of 10
`
`ADVANCED ENERGY INDUSTRIES INC.
`Exhibit 1009
`
`
`
`Zs/Zp = (Ns/Np)2
`
`or:
`
`Ns/Np = √(Zs/Zp)
`
`Zp represents the primary impedance, which is the output impedance of the driving source (Zg). Zs
`represents the secondary, or load, impedance (ZL).
`
`For example, a driving source’s 300Ω output impedance is transformed into 75 Ω by a transformer to
`match the 75Ω load with a turns ratio of 2:1:
`
`Ns/Np = √(Zs/Zp) = √(300/75) = √4 = 2
`
`The highly efficient transformer essentially features a wide bandwidth. With modern ferrite cores, this
`method is useful up to about several hundred megahertz.
`
`An autotransformer with only a single winding and a tap can also be used for impedance matching.
`Depending on the connections, impedances can be either stepped down (Fig. 10a) or up (Fig. 10b).
`
`Fig 10 . A singlewinding autotransformer with a tap can step down (a) or step up (b) impedances like a
`standard twowinding transformer.
`
`The same formulas used for standard transformers apply. The transformer winding is in an inductor and
`may even be part of a resonant circuit with a capacitor.
`
`A transmissionline impedancematching solution uses a λ/4 section of transmission line (called a Q
`section) of a specific impedance to match a load to source (Fig. 11):
`ZQ = √(ZOZL)
`
`Page 8 of 10
`
`ADVANCED ENERGY INDUSTRIES INC.
`Exhibit 1009
`
`
`
`Fig 11. A λ/4 Qsection of transmission line can match a load to a generator at one frequency.
`where ZQ = the characteristic impedance of the Qsection line; ZO = the characteristic impedance of the
`input transmission line from the driving source; and ZL = the load impedance.
`
`Here, the 36Ω impedance of a λ/4 vertical groundplane antenna is matched to a 75Ω transmitter output
`impedance with a 52Ω coax cable. It’s calculated as:
`
`Assuming an operating frequency of 50 MHz, one wavelength is:
`
`ZQ = √(75)(36) = √2700 = 52 Ω
`
`λ = 300/fMHz = 300/50 = 6 meters or about 20 feet
`
`λ/4 = 20/4 = 5 feet
`
`Assuming the use of 52Ω RG8/U coax transmission line with a velocity factor of 0.66:
`
`λ/4 = 5 feet (0.66) = 3.3 feet
`
`Several important limitations should be considered when using this approach. First, a cable must be
`available with the desired characteristic impedance. This isn’t always the case, though, because most cable
`comes in just a few basic impedances (50, 75, 93,125 Ω). Second, the cable length must factor in the
`operating frequency to compute wavelength and velocity factor.
`
`In particular, these limitations affect this technique when used at lower frequencies. However, the technique
`can be more easily applied at UHF and microwave frequencies when using microstrip or stripline on a
`printedcircuit board (PCB). In this case, almost any desired characteristic impedance may be employed.
`
`The next part of this series will explore more popular impedancematching techniques.
`
`Page 9 of 10
`
`ADVANCED ENERGY INDUSTRIES INC.
`Exhibit 1009
`
`
`
`Source URL: http://electronicdesign.com/communications/backbasicsimpedancematchingpart1
`
`Page 10 of 10
`
`ADVANCED ENERGY INDUSTRIES INC.
`Exhibit 1009
`
`
Accessing this document will incur an additional charge of $.
After purchase, you can access this document again without charge.
Accept $ Charge
Still Working On It
This document is taking longer than usual to download. This can happen if we need to contact the court directly to obtain the document and their servers are running slowly.
Give it another minute or two to complete, and then try the refresh button.
A few More Minutes ... Still Working
It can take up to 5 minutes for us to download a document if the court servers are running slowly.
Thank you for your continued patience.
This document could not be displayed.
We could not find this document within its docket. Please go back to the docket page and check the link. If that does not work, go back to the docket and refresh it to pull the newest information.
Your account does not support viewing this document.
You need a Paid Account to view this document. Click here to change your account type.
Your account does not support viewing this document.
Set your membership
status to view this document.
With a Docket Alarm membership, you'll
get a whole lot more, including:
- Up-to-date information for this case.
- Email alerts whenever there is an update.
- Full text search for other cases.
- Get email alerts whenever a new case matches your search.
One Moment Please
The filing “” is large (MB) and is being downloaded.
Please refresh this page in a few minutes to see if the filing has been downloaded. The filing will also be emailed to you when the download completes.
Your document is on its way!
If you do not receive the document in five minutes, contact support at support@docketalarm.com.
Sealed Document
We are unable to display this document, it may be under a court ordered seal.
If you have proper credentials to access the file, you may proceed directly to the court's system using your government issued username and password.
Access Government Site
