Homepage - RF Cafe
Webmaster: Kirt Blattenberger | KB3UON | Sitemap | ©1996-2014     Visit RF Cafe on
      Menu below is just a small sample of what is here!          Visit RF Cafe on Facebook Visit RF Cafe on Twitter Visit RF Cafe on LinkedIn
Custom Search
More than 10,000 searchable pages indexed.
•−•  ••−•    −•−•  •−  ••−•  •
RF Cafe Morse Code >Hear It<

Balanced Amplifier IP3 Improvement

Balanced Amplifier IP3 & P1dB Improvement Due to 90° Hybrid Couplers
by Thomas Shafer
NasonTek Services
(206) 920-5659

Balanced Amplifier IP3 Improvement Due to 90° Hybrid Couplers
A balanced amplifier design is defined by two amplifiers of equal gain, 1dB compression point (P1dB) and Third-Order Intercept (IP3), arranged in the configuration shown to the right. The couplers are 3 dB hybrids, where the input power is split equally between a 0°and a 90° port. The unused ports are terminated in the system impedance – typically 50 Ω. Reflections from the input and output ports of the amplifiers are shunted to the unused port of each coupler, giving the entire arrangement a matched impedance.

For a single, “unbalanced” amplifier, the output third-order intercept point is defined by the device specifications. The third-order intermodulation products (IM3) will appear at approximately 2Δ dB below the signal power of the primary tones at the device output where Δ = IP3in – Pin = IP3out - Pout (in other words, 3×15 dB below the output-referred 3rd order intercept point).

Balanced Amplifier IP3 Improvement Due to 90° Hybrid CouplersConsider the example of an amplifier with the gain and linearity specs shown above. If the input power of the two primary tones at ƒ1 and ƒ2 are both -30 dBm, then at the output, third-order Intermodulation products (IM3s) will appear at 2ƒ1 - ƒ2 and 2ƒ2 – ƒ1, at a power of:

IM3out = Pout - 2•(IP3out – Pout)
            = (Pin + G) - 2•(IP3out – (Pin + G))
            = (-30+24) – (2•(29 – (-30+24)))
            = -6 – 2•(29-(-6))
            = -76

When this amplifier is used in the balanced configuration above, the primary tones are split equally (-3dB) at the outputs of the first hybrid, with one signal phase-shifted 0°, and the other phase-shifted 90°. After the two split signals are amplified to [Pin –3dB + G], they re-combined, with the phase-shift swapped, so that the recombined signal is equal to [Pin + G] 90°.

However, since the input signal to each amplifier has been decreased by 3dB, the IM3s at the output of each amplifier have been decreased by 9dB. Specifically,

IM3out = Pout - 2•(IP3out – Pout)
            = ((Pin – 3dB) + G) - 2•(IP3out – ((Pin – 3dB) + G)))
            = ([-30dBm – 3dB]+24dB) – (2•(29dBm – ([-30dBm – 3dB]+24dB)))
            = -9dBm – 2•(29dBm – (-9dB))
            = -85dBm

The IM3s are combined in-phase through the output 3dB hybrid (remember the 90° phase shift is swapped), which is effectively adding 3dB to the number above. Thus the IM3s of the balanced amplifier are -82dBm, which is 6dB lower than the single amplifier.

The effective IP3out can be calculated with the formula

IP3out (dBm) = Pout (dBm) +0.5[Pout (dBm) – IM3out(dBm)]
                      = (Pin + G) + 0.5[(Pin + G) – IM3out]
                      = (-30dBm + 24dB)+0.5[(-30dBm + 24dBm) – (-82dBm)]
                      = +32dBm  3dB higher than the single amplifier                      QED


 
Here is a slightly different approach that springboards off of Thomas' work, but does not concern itself with the phases of the signals through the splitter and combiner. This solution is also valid using standard 2-way splitters/combiners with individual matched amplifiers that exhibit excellent input and output VSWR†.    --- Kirt Blattenberger

Assume individual device parameters are the same as in Thomas' example, and that Pin for each of the two system input signals is -30 dBm at the system input.

The 3 dB coupler splits the signals equally, so at the amplifier inputs the signals are -33 dBm.

3rd-order products at the output of each device are:

IM3out = Pout - 2•(IP3out – Pout)
            = 3Pout - 2IP3
            = 3•(-33dBm +24dB) – 2•(29dBm)
            = -27dBm - 58dBm
            = -85dBm

The IM3out after combining both amplifiers is -85dBm + 3dB = -82dBm

Now, since the gain of the balanced amplifier is the same as the individual devices, we have:

Gain = 24dB
IM3out = -82dBm
Pout = -30dBm + 24dB = -6dBm

Cranking those numbers back into the IP3 formula yields:

IP3 = 1/2 (3Pout - IM3out)
      = 1/2 (3•-6 - -82)
      = 32dBm                               QED (again)


Note: By a similar analysis, it can be shown that the 1 dB compression point (P1dB)
          also improves by 3 dB.





† Read about the characteristics of a 3 dB hybrid coupler that make it a great tool for building amplifiers
   whose individual devices do not match the system impedance, but do match each other's impedance.
A Disruptive Web Presence

Custom Search
Over 10,000 pages indexed! (none duped or pirated)

Read About RF Cafe
Webmaster: Kirt Blattenberger
    KB3UON

RF Cafe Software

RF Cascade Workbook
RF Cascade Workbook is a very extensive system cascaded component Excel workbook that includes the standard Gain, NF, IP2, IP3, Psat calculations, input & output VSWR, noise BW, min/max tolerance, DC power cauculations, graphing of all RF parameters, and has a graphical block diagram tool. An extensive User's Guide is also included. - Only $35.
RF system analysis including
frequency conversion & filters

RF & EE Symbols Word
RF Stencils for Visio

Product & Service Directory
Personally Selected Manufacturers
RF Cafe T-Shirts & Mugs

RF Cafe Software

Calculator Workbook
RF Workbench
Smith Chart™ for Visio
Smith Chart™ for Excel
Your RF Cafe Progenitor & Webmaster
Click here to read about RF CafeKirt Blattenberger... single-handedly redefining what an
                                 engineering website should be.

View the YouTube RF Cafe Intro Video Carpe Diem! (Seize the Day!)

5CCG (5th MOB): My USAF radar shop

Airplanes and Rockets: My personal hobby website

Equine Kingdom: My daughter Sally's horse riding website