Why use a butterfly stub instead of a normal rectangular stub?

A standard rectangular open-circuited stub acts like an RF short circuit when its length is exactly one quarter-wavelength. However, it is highly frequency-dependent. If the frequency shifts by 10 percent, the stub is no longer a quarter-wave long, and its impedance changes dramatically, ruining the match. A radial stub (shaped like a slice of pie) presents an RF short circuit over a much wider bandwidth because its varying width acts like an infinite series of stubs with slightly different resonant frequencies. A butterfly stub uses two of these radial stubs back-to-back, halving the total inductance to ground and creating an incredibly broadband, low-impedance RF short.

Where are butterfly stubs most commonly used?

They are heavily used in broadband RF power amplifiers, specifically in the DC bias networks. To feed DC power into an active transistor without letting the RF signal leak out into the power supply, designers use a 'bias tee' consisting of a quarter-wave high-impedance transmission line (acting as an RF choke) terminated with an RF short circuit. Because the amplifier must operate over a wide bandwidth (e.g., 2 to 6 GHz), a standard rectangular stub cannot provide an RF short across that entire range. A butterfly stub at the end of the bias line guarantees a solid RF short to ground across multiple octaves.

How do you define the geometry of a butterfly stub?

The geometry is defined by two main parameters: the radius of the sector, and the subtended angle. The radius determines the center frequency of the RF short (it roughly correlates to a quarter-wavelength in the dielectric). The subtended angle (how wide the 'wings' open, typically between 60 and 120 degrees) determines the bandwidth. A wider angle provides more bandwidth and a lower characteristic impedance at the connection point, making the RF short much 'harder' and more effective over a wide frequency span.

Passive Components

Butterfly Stub

An engineer designs a multi-octave power amplifier that must operate from 2 GHz to 6 GHz. To feed 28V DC into the transistor, they use a quarter-wave high-impedance trace terminated with an open-circuited stub to create an RF choke. They try using a standard rectangular stub to create the RF short. It works perfectly at 4 GHz, but at 2 GHz and 6 GHz, the stub's impedance shifts drastically, allowing RF energy to leak into the DC power supply and destroying the amplifier's gain. The solution is to replace the rectangular stub with a butterfly stub. By using two opposed radial sectors ("wings"), the varying geometry acts like a continuous spectrum of resonant lengths. It provides a near-perfect RF short circuit across the entire 2 to 6 GHz bandwidth, sealing the RF energy inside the amplifier and enabling true broadband performance.

Category: Passive Components

Geometry: Opposed radial sectors

Primary Benefit: Broadband RF short circuit

Stub Geometry Comparison

Stub Type	Bandwidth	Input Impedance (at resonance)	Primary Application
Rectangular (Straight)	Narrow (< 10%)	Low (Determined by trace width)	Narrowband matching, notch filters
Single Radial	Wide (~ 30%)	Very Low	General wideband biasing
Butterfly (Dual Radial)	Ultra-Wide (> 50%)	Extremely Low (Parallel stubs)	Multi-octave power amplifiers

Radial Stub Input Impedance Approximation:
Z_in ≈ -j · Z₀(r) · cot(k · r)
Unlike a straight stub where Z₀ is constant, the characteristic impedance of a radial stub drops continuously as the radius increases (the trace gets wider). This geometrically smooth impedance transformation provides the wide bandwidth.

Butterfly Angle Effect:
As the subtended angle (θ) of the butterfly wings increases, the effective characteristic impedance at the connection point drops, making the RF short circuit "harder" and the bandwidth wider.

Common Questions

Frequently Asked Questions

Why not just use a rectangular stub?

Rectangular stubs are inherently narrowband. They only act as a perfect RF short circuit when their physical length is exactly one quarter-wavelength of the operating frequency. If the frequency shifts, the stub's impedance becomes highly reactive. A butterfly stub uses radial geometry to provide a low-impedance short across a massive frequency range.

Why use two wings instead of one radial stub?

Placing two radial stubs back-to-back (the "butterfly" configuration) effectively places two broadband capacitors in parallel. This halves the parasitic inductance at the connection point, driving the input impedance even closer to a perfect zero ohms (an ideal RF short) than a single radial stub could achieve.

Where are they most commonly used?

In the DC bias networks of broadband RF and microwave amplifiers. The butterfly stub acts as the AC ground anchor for a quarter-wave high-impedance RF choke, allowing DC current to flow into the transistor while presenting a brick-wall reflection to RF energy attempting to escape into the power supply.

Related Terms

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Passive Design

Radial Stub Calculator

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