Handset PA Output Match: Reading Load-Pull Contours

What load-pull measures

A power amplifier does not have one fixed output performance. Its output power and its efficiency both depend on the impedance the output sees. Load-pull is the method that maps this dependence. It measures PA performance while varying the load impedance presented to the output.

For each load setting the bench records quantities such as output power and efficiency. The result is a set of numbers tied to points on a Smith chart. Drawing lines through points of equal value gives contours. Two families matter most here: contours of constant output power and contours of constant efficiency.

The result tells the designer which load the output matching network must create. The matching network is then designed backward from that target. For the network types, see RF Matching Networks: L, Pi and T Compared.

The Smith chart as the map

Every point on a Smith chart corresponds to one complex reflection coefficient Γ. For passive loads its magnitude is 1 or less, so all loads fall inside the unit circle |Γ| = 1. The centre represents the system impedance, for example 50 ohm, where Γ = 0.

Γ and the load impedance Z are related by:

and the inverse:

Here Z_0 is the system impedance. A load-pull plot is therefore a map of Γ. The distance from the centre is |Γ|. The angle around the chart sets the reactive part. A PA rarely performs best at the centre. Its best loads usually sit away from it, which is why a matching network is needed at all.

Why the two peaks sit apart

Each family of contours is closed and nested. The innermost contour of a family encloses the peak, and values fall off as the contours move outward. The two peaks do not coincide. The load giving maximum output power is generally not the load giving maximum efficiency.

The figure shows this layout. Solid lines are the output power contours, with the peak marked "max Pout". Dashed lines are the efficiency contours, with the peak marked "max efficiency". The shaded overlap is the "compromise load" region.

The reason is that the two goals ask different things of the output. Power is about how much signal the device delivers to the load. Efficiency is about how much of the supply energy ends up as signal rather than heat. A load that squeezes out the most power can also raise the dissipation in the device. Moving the load away from that point can save supply energy while giving up a little power. So the two peaks separate.

The shape of the contours also carries information:

• Tightly packed contours mean performance changes quickly with load. The design is sensitive to mismatch.
• Widely spaced contours mean a forgiving load. Small errors in the match cost little.
• Elongated contours show that the load can move along one direction cheaply but not across it.

Picking a compromise

The designer overlays both families and looks for the region where both stay close to their peaks. That region is the overlap of one power contour and one efficiency contour. A point inside it gives up a little of each quantity instead of all of one.

The choice depends on the product goal. If output power is a hard requirement, the point moves toward the power peak. If battery life matters more, it moves toward the efficiency peak. The data show the trade, but the weighting is an engineering decision.

The second figure shows the same idea along a single line through the chart. Output power and efficiency are plotted against load position. Each curve peaks at a different place. A vertical line between the peaks marks the chosen compromise, and the dots show what is given up in each quantity.

Worked example from the reflection coefficient

Take a 50 ohm system. Suppose, as a made-up illustration and not a measurement, that a load-pull sweep along the real axis put the power peak at 25 ohm and the efficiency peak at 100 ohm.

The reflection coefficients are:

• At 25 ohm: Γ = (25 − 50) / (25 + 50) = −1/3, so |Γ| ≈ 0.333.
• At 100 ohm: Γ = (100 − 50) / (100 + 50) = +1/3, so |Γ| ≈ 0.333.

The peaks sit on opposite sides of the centre at equal distance. The midpoint in Γ is Γ = 0, which is 50 ohm. In this example the midpoint happens to land at the centre because of the numbers chosen. It is not a general rule.

A point at the midpoint sits one third of the way, in |Γ|, from each peak. The designer then reads the power and efficiency values at that point from the contours, and checks that the losses against each peak are acceptable.

As a check on the mismatch itself, the fraction of power not reflected at |Γ| = 1/3 is 1 − |Γ|² = 1 − 1/9 = 8/9, about 0.889. Here the PA is not simply being matched for maximum power transfer to 50 ohm. The target load is a deliberate choice, and the measured contours replace the textbook rule.

What to carry into the design

Read the contours as a trade map, not as a single answer. Find both peaks, find the overlap, then choose a point and note the cost in each quantity. The matching network must then present that load at the PA output over the band the product needs. For the chart reading itself, see Smith Chart Basics: How to Read Impedance and Reflection.

In plain words · for students and beginners

Load-pull contours in plain words

An everyday picture

Think of a hill map with two hills. One hill is "most power". The other is "best efficiency". The lines on the map join places of equal height. The hills stand in different spots, so no single place is the top of both.

Standing on the saddle between them, you are fairly high on both. You are not at either top. That saddle is the compromise load.

Where the picture breaks down: a real hill map is flat paper, but the Smith chart is a map of impedance. Each spot on it stands for a load, a number with a size and a phase, not just a place.

The same example, step by step

1. The system is 50 ohm. The centre of the chart is 50 ohm.
2. Pretend the best power is at 25 ohm and the best efficiency is at 100 ohm. These are made-up numbers.
3. Turn each into a reflection coefficient, which is a number saying how much wave bounces back. 25 ohm gives −1/3. 100 ohm gives +1/3.
4. The two peaks are on opposite sides of the centre, the same distance away.
5. The point halfway between them is the centre, 50 ohm. That happens here only because of the numbers chosen.
6. Read the power and efficiency at that point. Both are a bit below their peaks. That small loss is the price of the compromise.

Mistakes beginners make

• Thinking the best power and best efficiency are the same load. Generally they are not.
• Treating the centre of the chart as the goal. The PA often wants a load away from the centre.
• Choosing a point without checking what it costs. Always read both values at the chosen point.
• Forgetting where the load was measured. If the reference point moves, the contours move with it.

Remember

• Load-pull measures PA performance while the load impedance is varied.
• The power peak and the efficiency peak are generally at different loads.
• A compromise load sits in the overlap and gives up a little of each.

Related pages on RF View

• Smith Chart Basics: How to Read Impedance and Reflection
• RF Matching Networks: L, Pi and T Compared