In Directional Couplers, Quadrature Hybrids

The most common question we receive about our stripline directional couplers, low loss airline directional couplers, and high directivity directional bridges is ‘How much power can it handle?’. The reason is that directional couplers are frequently used for load-pull testing of amplifiers or monitoring a signal after a power amplifier. In either case, the directional coupler will be placed as close to the output of the power amplifier as possible, which means it must perform within spec at high operating powers.

Despite the importance of directional coupler performance under high power inputs, most directional coupler vendors offer a single number without any background or context. As we will show in this post, the static value commonly provided for the power handling of a directional coupler is an oversimplification of the matter.

typical-directional-coupler-use-case

Directional Coupler Failure Modes

There are two types of power handling limits frequently cited depending on the time scale and the failure mechanisms.  Average power handling refers to the ability of the device to handle a high level of power on a long time scale, which can be limited by heating in the device, power limits of the internal termination, or saturation of magnetic material inside the device. At very high temperatures in excess of 300 C°, the Teflon dielectric in the stripline couplers may pyrolize or burn, and solder can soften. But even at lower temperatures the difference in coefficient of expansion of different materials can cause the materials to shift, sometimes catastrophically, and render the part inoperable. Most Marki directional couplers are bidirectional, so the user can supply a termination that will accept the amount of power necessary. When used in a 50 Ω system to measure forward power, this limit is very low. Situations where a higher power termination is required are discussed later. The CBR series of high directivity bridge couplers are the only Marki directional coupler products with either magnetic material or internal resistive terminations, and in this case the resistors would exceed their power rating before the magnetic cores are saturated.

On a shorter time scale peak power input limits are caused by voltage breakdown of the dielectric. This lead to instantaneous, catastrophic failure. However, this failure only occurs at extremely high voltage levels. For example, Rogers 4003C, a common RF material, has an ‘Electrical Strength’ of 780 V/mil. This means that a directional coupler built using 8 mil Rogers 4003C would have a breakdown voltage of over 6 kV, giving a voltage breakdown of around 88 dBm (800 MW) of instantaneous power. This is obviously a ridiculous value, and something else would break before reaching this power level, most likely the connectors.

directional-coupler-sources-of-failure

In addition to catastrophic failures, which lead to permanent inoperability of the directional coupler, there are also soft failures. This is where the part temporarily falls out of spec under certain parameters of operation, such as the insertion loss increasing beyond acceptable limits under high power. Though less disastrous because a soft failure does not necessarily require replacement of the directional coupler, it is just as important to be aware of soft failure parameters to know when to question the results of a measurement. The most common soft failure in a directional coupler is when the temperature rises in the part and the materials inside expand at different rates. This causes a deviation of the geometry from the design and changes the performance of the directional coupler. This is different from the temperature cycling described in the paragraph about catastrophic failures because, as the part cools down, it returns to specification.

There are two more considerations for directional coupler failure modes. All of the failures discussed so far have related to the circuit inside the housing. It is likely that failures will frequently occur instead in the connectors or the transitions from the connectors onto the circuit (the pin to circuit transition). Which connector to select when purchasing a directional coupler is therefore a more important consideration than it would be for other components such as power dividers or filters.

In addition to the connectors, a 50 Ω load is frequently used on the isolated port of a bidirectional coupler when it is only used to measure power in the forward direction. When used in a well matched environment this load will see very little power, and its power handling is not an issue. However, this termination is frequently the limiting factor for average power when the directional coupler is used in a non 50 Ω system (i.e. in a load pull measurement or when used between the power amplifier and a mismatched antenna). In addition to the 50 Ω load, the overall average power handling of the coupler is degraded by the extra loss in the coupler. If the return loss seen at the output is 0 dB, then the power dissipated in the mainline will be nearly doubled.

Expected Power Handling of Marki Directional Couplers

Marki sells several types of directional couplers with varying methods of construction and varying power handling expectations:

Directional Coupler Construction Achievable Directivity (dB) Coupler Values Connector Options Expected Average Power Limit
Stripline Directional Coupler 16-22 9,10,13,20 SMA, 2.92, 2.4, 1.85 20-100W
Stripline Dual Directional Coupler 23-25 10 SMA 20-100W
Airline Directional Coupler 22-24 Variable N, SMA, 2.92, 2.4 15-500 W
High Power Stripline Directional Coupler 20 17 SMA, APC-7 60-200W
High Directivity Bridge Coupler 32-40 16 SMA 1W

Stripline directional and dual directional couplers use a triplate stripline technique. They are available with all standard Marki connector options, and with flat coupling values and high directivity. The power handling of these directional couplers will be discussed and tested extensively later in this post.

Airline directional couplers use an air dielectric to minimize loss and maximize power handling. They are available in standard connector configurations as well as with N connectors. These also have excellent directivity, but the airline construction leads to a sloped coupling value characteristic of a single stage directional coupler.

High power stripline couplers are built with wide lines and thick dielectrics to minimize loss and offer high power handling, but with a flat coupling value. They are available with SMA or specialized APC-7 connectors to further minimize adapter loss with various test equipment.

High directivity bridge couplers are built as a resistive bridge with a balun. These offer extremely high directivity for return loss measurements, but they have very limited power handling due to the resistors absorbing half the power.

As we will see in the testing section, the power values quoted are extremely speculative, and depend intimately on the test environment and frequency of operation. Actual estimates for the power breakdown of a coupler in a test system requires consideration of a few factors that we will present.

Average Power Testing of a Stripline Directional Coupler

Steady State Temperature vs. Input Power

In our testing we were interested in characterizing limits on average power handling for our most common directional coupler construction, the triplate stripline. Before we begin testing, we have to understand the thermodynamic system of the C13-0140 directional coupler we were testing and its environment. Temperature differences between two media lead to heat flow. When a coupler settles at a temperature difference between the coupler surface and its surroundings for a given input power level, this means that the rate of heat flowing from the coupler into its surroundings is the same as the rate at which the coupler generates heat.

directional-coupler-power-flow-fix

Where does this energy come from? Dissipative loss in the striplines converts electrical power into heat. Therefore, the insertion loss (less the return loss) manifests itself as the heat generated by the device. As input power increases, more power is dissipated in the lines of the directional coupler. This converted energy heats up the component using the lines almost like the filament in a lightbulb. For example, putting +40 dBm (10W) into a directional coupler with a 1db insertion loss and no return loss means that 2W of power is being dissipated through the striplines.

To create our testing setup, we needed a LOT of power. The final setup consisted of two high power amps, both heatsinked, a power meter, an oscillator, and two additional directional couplers designed for high power handling. The CA-40 and CA-18 are both excellent choices for high power testing due to their extremely low loss and low dimensional mismatch due to the air dielectric. The block diagram of the setup can be seen below with numbers in dB.

high-power-test-path-block-diagram

With this setup we can deliver a maximum power of 50 W into the test device. The power heads cannot handle such high power, so we heavily attenuate before measuring the output power. On the input side we used a CA-40 airline directional coupler as an input monitor and on the output side a CA-18 airline directional coupler as an attenuator. The temperature change of CA-18 is negligible during our tests and the CA-40’s air-line design means its insertion loss and coupling values do not vary over the temperatures we are testing the C13-0140. At 5.7GHz, the insertion loss and coupling value of the CA-40 are the same at room temperature and at 46 °C. This means that we can trust any changes in loss to be due to the DUT only and not the air line directional couplers.

With everything set up we can test. The directional coupler was suspended in room temperature air with no heatsink. The graph of average power input vs. settling temperature is shown below for a C13-0140 directional coupler.

marki-c13-0140-temperature-vs-input-power

The fit is very linear with a temperature/power coefficient of .56 C°/W. The constant value 27˚is the ambient room temperature. Though this room temperature seems high, the directional coupler is in contact with a warm power amplifier and receives the exhaust from the heatsink of the amp, which raises the temperature of its surroundings quite a bit. Depending on the environment in which you are using the directional coupler, you can bump this fixed offset up or down by changing the ambient temperature.

You can change the temperature/power coefficient by heatsinking the coupler, or by cooling the outside environment; this is because heat flow is proportional to the temperature difference, not the absolute temperature Applying a heatsink allows more heat to flow out of the coupler per second. The maximum amount of power you can put into a coupler is based on the environment you operate the coupler in. You can put a lot more power into a coupler that is being actively cooled versus a coupler that is being operated in the middle of summer in a Walmart parking lot in Phoenix, AZ.

Time Response of Temperature to Time Varying Inputs

Generally a coupler is not used with a constant sinusoidal input.  Frequently the power in a high power setup is ‘pulsed’, meaning that it is run at maximum power for a period t0 and then turned off for a period t1 to allow the components to cool. The ratio of t0/(t0+t1) is called the duty cycle. How should an engineer determine how long t0 and t1 and what the duty cycle should be?

If the pulses of peak power are on the scale of the temperature settling time of the directional coupler, the temperature of the device can vary quite a bit. We can visualize the directional coupler as a heat based capacitor that will exponentially rise or fall to an equilibrium temperature based on the input power it receives at that time.

τ is the time it takes the directional coupler to rise from a starting temperature to the steady state temperature at the new power. As you can see in this visualization, in the case of the red temperature plot the difference between peak and average temperature is quite large. This is why it is important to also know the step response of temperature to power. The green line depicts when it would be safe to use average temperature to estimate the maximum temperature of the directional coupler. These plots are defined by a rise time tau which we will discuss in depth later on.

To test the step response, I allowed the directional coupler to settle at an equilibrium temperature and then stepped the power input up and tracked the temperature of the coupler until the rate at which the temperature changed slowed down to 0.1 C°/minute.

stacked-matlab-pics

 

In the plots above you can also see the data fitting equations and their respective plot. We theorized that the mathematical form of the temperature settling would be temperature-equation. Trepresents the initial temperature and T1 represents the final settling temperature. τ is the time settling constant in minutes, which defines how long it takes the directional coupler to rise from Tto T1. It takes longer for the temperature to settle for a jump from 4.4 to 14 watts than a jump from 14 to 37.5 watts. Though we can’t define a pure static τ, we can still see what order it is on, which is around 5 minutes. Since we have a general idea of the scales at which the transient temperature response matters we can now define when it is ok to use average power values to determine the maximum temperature of the directional coupler and when it would be necessary to do further calculations. If your pulse duration or random power fluctuations last for much less time than τ you can simply use average power to predict the maximum temperature, otherwise you cannot.

Directional Coupler Performance Response to Varying Input Power

Now we have fully characterized temperature operation of the device; we still need to know how the temperature will affect the user. This means looking at the specs of the part at the different temperatures to relate the performance of the part to the input power level. In our testing of the C13-0140 directional coupler, we logged steady state values of insertion loss, coupling loss, and directivity.

c13-0140-coupling-vs-input-power c13-0140-return-loss-vs-input-power c13-0140-insertion-loss-vs-power

c13-0140-directivity-vs-input-power

Insertion loss goes up as we increase the input power and with that, the temperature. This is exactly what we expected because increasing the temperature increases the resistance of the striplines. The coupled power shows minimal variation with a slight tendency to couple less power as temperature increases. Most surprisingly at 5.7 GHz, increasing input power improves the directivity. Directivity is the most sensitive spec to design parameters so small changes in the physical dimensions of the directional coupler can create drastic changes in directivityAt this frequency the directivity happens to increase with increasing power, most likely due to a shift to higher frequency as the coupler expands moving the directivity down the curve. The return loss is constant against input power.

Here is a measurement of the C13-0140 performance parameters (Return Losses, Coupling Factor, Insertion Loss, and Directivity) before:

c13-0140-s-param-before

And after power testing:

c13-0140-s-param-after

All specs are still approximately the same after putting 50W of power into the part at 50 °C. This demonstrates that operation of up to 50 watts of power at 5.7 GHz will not cause permanent variation of any of the directional coupler specs.

At such high levels of power even small fluctuations in the dBm values result in large differences in linear power. Most RF and microwave measurements are expressed in a logarithmic scale (dB, dBm, dBc) due to the wide dynamic range of most measuring instruments. When using linear measurements for doing power studies, small variations in the logarithmic units express as large variations in linear power levels. For example, the difference between 47 dBm and 46.5 dBm on a watt scale is around 5.45 watts. This is one reason that it is very important to make these measurements with extra care. Ideally, every stage in the test path would be fully characterized along the full dynamic range of power but this would be almost impossible; the physical parameters of the system are constantly changing and dynamic power characterizations can change for reasons that are not immediately apparent. Extra attention must be given to each connection from a component or a cable to ensure that all of the components are operating as designed.

Conclusion: How do you determine if a directional coupler is suitable for your requirement?

We have proven that the C13-0140 directional coupler will survive at least 50W of input power with minimum degradation in specs. We could not test to a higher power level, since we did not a higher power source or higher frequency amplifier available, but if we did how much power could it have accepted?

If we use the stated operating temperature range of Marki components as a guide, then 100˚C is the typical cutoff temperature. If we use this as the limit, then the coupler could theoretically accept 128 W of power. This is assuming that all of the loads remain 50 Ω, that the insertion loss did not increase significantly as the power increased, and that temperature of the pins or the stripline that are radiating heat are not significantly hotter than the case. Some of these assumptions may not be valid, which is why it is safer to back off the max power input to something more conservative like 100 W or less. However, we know that the couplers can handle much higher temperatures than 100˚C, and in a heatsinked environment it is likely that the directional coupler could survive much higher power.

How do you determine if a given directional coupler will work for your application? The most reliable way is to input lower levels of power than you plan to use, and test the temperature response of the directional coupler. This is not a guarantee, but it will give you a good idea of what to expect.

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