Tag Archives: PowerDividers
One of the unique products that we have at Marki Microwave is our broadband, high isolation 3-way and 4-way power dividers. In this blog post we will answer some common questions we receive, including:
- How to make a 5 way power divider
- How to make a 6 way power divider
- How to make a 7 way power divider
- How to make an 8 way power divider
- How to make a 10 way power divider
- How to make a 12 way power divider
- How to make a 16 way power divider
- How to make a 32 way power divider
- How to make an n way power divider
Yesterday I wrote about how it was possible to create a PAM4 signal using a Wilkinson power divider. Our Wilkinson product line also includes more rare 3 and 4 way power dividers, which means that we can combine more than two signals together, making higher order amplitude modulation possible.
To review, here is how to make a four level pulse amplitude modulated (PAM4) signal from a single PRBS generator:
You just take a PRBS signal, decorrelate it from itself, attenuate one signal by 6 dB, phase align them, and then recombine them. It’s really pretty easy if you have all the components. The other option is to use two data sources with the amplitudes already set to the correct value, with common clocks to align the signals in time. Here is what you get:
So how to make a PAM8 signal? Just add another PRBS signal, but this time it has to be attenuated by another 6 dB. To recap, a PRBS signal, a different (or uncorrelated) PRBS signal with 6 dB lower amplitude, and another different PRBS signal with 12 dB lower amplitude walk into a bar, and out comes a PAM8 signal:
Not that great. It is a PAM8 eye diagram for sure, but it doesn’t look that nice. This is because the phase decorrelators I was using had a lowpass response, as well as the multiple reflections present in my combination system. So it’s possible to do some crude testing using this setup, but I wouldn’t recommend it for any postdeadline OFC papers.
Personally I don’t like PAM modulations, especially above PAM4. At least with PAM4 you get twice the number of bits, but with PAM8 or god forbid PAM16, you are sacrificing a big chunk of your noise margin (remember the spread on each of the eyes is gaussian) for an improvement of only 50% or 33%, not an order of magnitude or anything like that. I think it is much more promising to use either the phase of the optical carrier itself or an electrical carrier on the signal for doing IQ modulation in interesting ways. Speaking of IQ modulation, we sell some excellent IQ mixers that would be perfect for that. Contact firstname.lastname@example.org to learn more.
After investigating and concluding that yes, Wilkinson power dividers work for splitting data, the natural question was whether they work for combining data.This is a more complicated question for splitting data. For one thing, the role of isolation was unclear. Also the implications of the return loss increasing at lower frequencies was unclear. Furthermore, I didn’t know when anyone would want to combine two baseband signal together.
Today I found answers to all of these questions. To accomodate increasing datarate requirements, signal integrity engineers are transitioning from on-off-keyed (OOK) to pulse amplitude modulated (PAM4) signals. The difference is that OOK uses two signaling levels (for 1 and 0), while PAM4 has 4 levels (for 11, 10, 01, and 00). Therefore PAM4 can transmit 2 bits per symbol in the same amount of time OOK transmits 1 bit, thereby doubling the datarate.
In order to create a PAM4 signal using OOK test equipment, the technique is to attenuate one signal by 6 dB in power (to create 1/2 the voltage signal) and combine it in phase with another signal using a power combiner! Here’s my chance to test my theories. Would a Wilkinson create an intelligible eye diagram using PAM4, or would it highpass filter it somehow? What would I see?
First off, here is the PAM4 signal using a resistive power divider, the PD-0030, running at 13 GS/s. All eyes are taken with a 2^31 PRBS pattern with significant low frequency content.
There is some distortion, but the eyes are open. The amplitude of the middle eye is different from the outer eyes because the amplitudes were not tuned to be perfect, and I’m not sure what the optimal amplitudes (they need to be optimized with respect to the noise in the system). The distortion could come from the return loss in the power divider, the lack of isolation in the power combiner, or the high pass filtering from the cables used to create the signal. I didn’t investigate to find out.
Now here is the output from a Wilkinson, the PD-0220, of the same signal:
Booyah. Not only is the eye open and legible, it looks better than the PD-0030 eye. It has a higher amplitude due to the lower loss of the Wilkinson, and it might also look better due to the improved isolation reducing some of the reflections. The important thing is that it looks better than the resistive.
Now this is the result of a 2-20 GHz Wilkinson. As I stated, this is a 2^31 PRBS pattern, which at 13 GHz means that most of the spectral power density is below 4 GHz. Maybe the 2-20 GHz Wilkinson was masking the distortion it introduced. So I tried the same experiment with one of our surface mount PD-0434 Wilkinsons in a test fixture:
As you can see, it still works. The amplitude is the same as the PD-0220, which is higher than the resistive PD-0030. There is some additional distortion, which may be from the lower isolation of the PD-0434 vs the PD-0220, or it may be from the degraded return loss from the surface mount transition.
What if we go really crazy, and put all of the signal outside the ‘band’ of the Wilkinson? Here’s the PD-0434 creating a 4 GS/s PAM4 signal:
Still looks beautiful. So there you have it. You can use Wilkinsons for almost any task you have in signal integrity. I prefer Wilkinsons because they have 3 dB less loss than resistive power dividers, meaning that you get twice as much power output from them, and they have isolation, which tends to calm down resonances in a system. If you like your resistive power dividers, you can stay with them. When you are trouble shooting or optimizing your experiment or system, it’s probably worth it to look at both.
In making the datasheets for the first Microlithic frequency doubler (MLD-1640), it occurred to us that not enough has been made about the difference between isolation and suppression.
In mixers and amplifiers, some parameters are expressed relative to the input powers, while some are expressed in terms of the output power, with the conversion loss or gain calibrated out. This includes third order intercept point (IP3), which can be expressed as either input IP3 (IIP3), or output IP3 (OIP3). In general it is better to use OIP3 for mixers, since what really affects the dynamic range of a system is the amplitude difference between the output signal and output spur, expressed in dB relative to the output signal or carrier (dBc). This is illustrated in the table below, where the difference between the T3 and competing mixers is even greater when the superior conversion loss of the T3 is considered.
|T3-05||33 dBm||6.5 dB||26.5 dBm|
|Imitator 1||25 dBm||10.7 dB||14.3 dBm|
|Imitator 2||30 dBm||9 dB||21 dBm|
Note that it is better to use IIP3 in amps, for the opposite reason, namely that you want to give the amp credit for it’s gain. So in parts with gain the appropriate measure is IIP3, while in parts with a loss the appropriate spec is OIP3.
When the same logic is applied to spurious products in mixers and multipliers, the input referred value in dB is called isolation, while the output referred value in dBc is called suppression. Suppression is the preferable number to use, because it expresses the important value to the system. The isolation can always be improved by increasing the conversion loss of the mixer or multiplier, but this is obviously undesirable. There are, however, some issues using suppression.
The first comes with mixers. In all mixers we express the spurious output of the LO in terms of isolation, since it is dependent on the input LO power. Since the LO power does not change the conversion loss referenced to the input, this means that the suppression can vary by several dB with different LO drive levels.
The second complication is that the input signal, converted signal, and spurious tone are all at different frequencies. For example, when using a doubler with an 8-20 GHz input range, the output doubled frequency is 16-40 GHz, and the undesired tripled frequency is 24-60 GHz. This means that the isolation curves look like this:
While the third harmonic suppression looks like this:
The curves look slightly different. The suppression is more stretched out, and distorted by the curve of the conversion loss of the doubler. This is the result of the suppression calculation, which can basically be thought of as a 1:1 mapping of the isolation through the conversion loss.
I was thinking about the difference between power dividers, baluns, and couplers, and realized that they could all be thought of as power splitters. The characteristics that make them different are the relationship between the outputs in terms of amplitude, phase, and attenuation between outputs. Here is a brief chart that explains them all:
When you master phase, you become like a God, capable of performing wonders that mere mortals can only dream of. Wonders like making laser beams (using phase engineered quarter-wave reflectors), communicate tremendous information great distances through thin air (all modern communication formats use both amplitude and phase), and create amazing products (balanced amplifiers, balanced mixers, phased array antennas, Mach Zender modulators, the list never ends).
BUT…phase is the hardest thing to understand in microwaves, RF, and photonics. It is hard to measure, hard to visualize, and makes some very confusing homework problems that kept me in the late night coffeeshops of Champaign-Urbana well past my bedtime.
In this post we will make a dent in the universe of phase understanding by clarifying the difference between phase and group delay, and in the process explain why you can’t match phase with variable line lengths. When you buy a phase shifter, it is sometimes what I would call a real phase shifter, and sometimes what I would refer to as a ‘group delay shifter’. The trombone type variable delay lines (we like the ones from sage) are actually variable time delay elements, and not phase shifters.
A group delay (or time) shift is easy to understand: it is how long the pulse (or wave) takes to arrive at your measuring receiver. Differential delay is therefore the difference in how long it takes for two pulses or waves to arrive. In passive components it is just the distance divided by the speed of light (or whatever your wave is) at your frequency in your material.
Phase is much more difficult. It is the integral of group delay over frequency (plus an offset), or differently the group delay is the derivative of the phase vs. frequency. This is why filters can be used as time delays; the edges of the filter have significant phase variation that leads to significant group delay variations over a narrow bandwidth (this is called Kramers-Kronig relation).
A variable length delay line, therefore, can only change the phase by changing the group delay. But by changing the group delay, you are changing the integral (slope) of the phase vs. frequency. This means that the phase change will be different at different frequencies. This is very different than what you get from a quadrature hybrid coupler, or a balun, where the phase shift is constant across frequencies. The difference is shown below. First is a plot of the phase difference between the two outputs of a BAL-0520 Balun (180°), a QH-0226 quad hybrid (90°), a coupler plus two 37.5° Schiffman phase shifters we developed as a custom (165°), a PD-0220 wilkinson power divider (0°), and a PD-0220 with an extra .570″ adapter on one side (variable).
As you can see, the phase is flat across the bandwidth of the device for everything except the PD-0220 with the extra delay line (adapter). This has a rapidly changing phase across frequencies. If we take the derivative of this we should get the group delay, but instead I measured the differential group delay with the PNA-X.
Here you can see that the differential group delay between outputs for each of the devices is 0, except for the power divider with the adapter, which has a flat constant group delay (ignore the big hump, I think that is from the calculation the PNA is doing with the phase flip).
So what is the lesson? You can phase match two outputs using a variable delay line, but only at a single frequency. Otherwise you have to do it with a coupler, a balun, a Schiffman, or some other true variable phase circuit.
The reactive power splitter is like Rodney Dangerfield: it gets no respect. Often people will resort to the primitive, high loss resistive power divider simply because a Wilkinson is specified over a limited band, not down to DC. Don’t get me wrong, resistive power dividers have their place. They are much cheaper, anyone can make them, and they can cover very wide bandwidths when made properly.
The truth, however, is that a Wilkinson will work for one application very well outside of the specified bandwidth. The application it will work for is splitting a signal into two well matched loads. While it is true that you can’t have a reciprocal, lossless, and matched three port device in general, you can have such a device if the output ports satisfy one condition: they must be common mode or differential mode. That means that the signals need to be identical to each other (common mode) or opposite of each other (differential mode).
This happens all the time when someone is trying to split an incoming signal into multiple well matched loads. This is why our baluns work so well for so many people. While they don’t have any isolation, and the return loss from a single ended signal put into one output port is terrible (3 dB intrinsically), they are usually used by people to input data to a chip for testing, or combining the differential outputs of a chip. In this case the return loss looks good all around. In contrast, if they were used to combine identical outputs from a chip, then it would be pure reflection. A balun looking into an in phase power divider just looks like an open circuit.
This brings me to the Wilkinson. Outside of the specified band, the Wilkinson will have no isolation and work just like a reactive power splitter. It will have 3 dB nominal splitting loss, but no additional loss (unlike a resistive power divider). If you are using it to split an incoming sine wave, it will work beautifully, as long as the frequency isn’t very, very low (below tens of MHz). Since the group delay and insertion loss are flat, it can also be used to divide data.
Here is the eye diagram from our PD-0020, a resistive power divider:
This is from a 10 Gigabit per second, 2^31 length psuedo-random bit sequence (PRBS) pattern, so there is significant low frequency content. The input eye is saved in the background. As you can see, the output is very clean, but with significant attenuation (1/2 the voltage). This is typical of a resistive power divider.
Next up is the output from a PD-0140. This has a 40 GHz high frequency cutoff, well above what we need to pass 10 Gb/s data, but the 1 GHz low frequency cutoff is high enough that some data will fall beneath this frequency. Here is the output:
The eye looks pretty open. There is some small overshoot associated with some group delay variation, but nothing too bad. The inside of the eye is wide open. If the low frequency content was compromised, we would see baseline wander. Since the eyebrows are just as narrow as with the PD-0020 case, we conclude that there is no significant low frequency content degradation.
Fair enough, but maybe the data slipped under the 1 GHz limit. Maybe the part has a conservative spec. Next we try the PD-0218, a Wilkinson power divider with a 2 GHz low end cutoff, well above a good amount of frequency content in a 10 Gb/s signal:
Once again, narrow eyebrows, no low frequency content distortion. Once again, there is some wiggle in the eyebrows due to group delay flatness. It is true that the group delay will not be quite as flat in a Wilkinson as a resistive power divider. This is an inevitable result of the fact that a resistive PD is just shorter than a Wilkinson, and the impedance transformation is performed resisitively instead of reactively. The tradeoff is that the voltage out from a Wilkinson is .707 times the input, vs. .5 times the input for a resisitive.
Is there some point at which the low frequency content will eventually catch up to us? Yes there is. At some point the Wilkinson’s reactive impedance match will no longer work, and the input sees a 100 ohm load that it just reflects from, causing significant problems. This frequency is very low compared to the operating frequency of the power divider, though. To illustrate, here is 100 Mb/s data passed through the same PD-0218:
At this point you can see some degradation in the eyebrows due to the Wilkinson power divider. So if you are trying to push data from lower than 100 Mb/s through the same system as 40 Gb/s data, then you’ll have to use the resistive.
When I first entered the world of mixers, customer concerns about spurs were very cryptic. When one spur mattered against another seemed totally arbitrary. Over time I learned that certain spurs matter in certain situations. Here are those situations:
1 LO x 0 IF/0 RF (LO-IF/RF Isolation): As we discuss in the mixer basics primer, this matters all the time, but particularly in an upconversion with a low frequency IF. In this case the LO will need to be filtered from the nearby RF. This is actually a good reason to use a lower frequency IF before final transmission, since that makes the final stage filtering easier. The LO – IF can also be a problem in conversions with a high IF.
1 RF x 0 LO (RF-IF isolation): This isolation, like the LO-IF isolation, is important in conversions with a high IF frequency. For example a DC-6 GHz up/downconversion to 7-13 GHz will need the RF/IF filtered out of the output.
1 LO x n IF: This spur is important in the same situation: upconversion from a low frequency IF. In this case the LO will be on the inside of the LO + IF and LO – IF, and the other side will be the LO + 2 IF or LO – 2 IF, as below:
This is an upconversion of a 20 MHz IF with a 6 GHz LO using an ML1-0220L. You can see that the LO is suppressed due to the RF-IF isolation, and the 1 LO x 2 IF is suppressed due to the balance of the mixer.
2 RF x 2 LO (also m LO x m RF): This is the brother of the 1 LO x n IF, but for downconversions. In a downconversion to a low IF, the 2×2 will show up at double the IF frequency, and requires a low pass filter between the IF and 2IF.
m IF x 0 LO (Harmonic IF Isolations): This is important for medium to high level IF frequencies translated to low to medium level RF frequencies. For example, a 1 GHz IF translated to a 3 GHz RF will have to contend with the 3xIF harmonic, which is probably fairly strong. Odd harmonics, in general, are stronger than even harmonics.
n LO x 0 IF (Harmonic LO Isolations): These are generally only a problem for band conversions, usually for satellite work. If the LO is lower than the IF or RF, then it becomes a problem similar to the harmonic IF isolations, but worse because the LO is stronger. The 2LO can be a problem for high IFs as well.
2LO x n IF: These are an issue when doing a low side upconversion. The LO – 2,3,4 IF will cross the fundamental when the IF increases high enough, as shown below (from our spur calculator):
n RF – (n-1) LO: These will show up in a typical downconversion with a high side LO:
n LO – (n-1) RF: These, similarly, will show up in a low side LO downconversion:
Other spurs will show up in many disparate situations, with differing levels, particularly in unusual conversions. One conversion that you haven’t seen mentioned much in this blog entry? The high side upconversion. This is because the high side upconversion is the frequency translation with the fewest spurs:
In this case the only interfering spur is the 3rd harmonic of the IF, and that is relatively low level. The high side upconversion causes a reversal of the frequencies, so we recommend a heterodyne system with a high side upconversion to a high IF, filtering, andd then a downcoversion to a lower IF for final processing. The other downside? You need a wideband mixer to use the high frequency LO. A wideband mixer much like the ones sold by Marki….
We get this question a lot: how much power can part XYZ handle?
Power handling is a difficult topic, because the ways in which a device can fail depend so much on the operating conditions that it is subjected to.
We specify the max power on (for example) the PD-0165 as 1 watt only to be extremely conservative. Here are some use scenarios for the PD-0165 and the power handling I would estimate:
– Ideal use case: 50 ohm matched at all ports, using the device as a power divider. In this case the device is only dissipating the excess insertion loss. Depending on the heat sinking it has attached, it should be able to handle 10s of watts of CW power or more at 43 GHz. At a high enough power the connectors will fail.
– Worst case CW performance: Out of phase reflections at both output ports, or use as a power combiner with two signals that are 180° out of phase. In this case all the power will be dissipated in the isolation resistors, which means that the power is limited to what the resistors can dissipate. This is where the power handling will be limited to about 1 W before the resistors pop.
– Pulsed case: In this situation the power is limited by the voltage breakdown in the device. If the peak power is high enough the voltage will break down the dielectric either in the connectors or the substrate, this isn’t clear. The amount of power it can take depends on the pulse width and hence the peak power.
So the amount of power that you can put through the device depends on how you are using it and how much heat sinking you provide to it.
On Tuesday, while we were debating over the theoretical explanations of the mega-high linearity T3 Mixer, Ferenc asked me to answer a seemingly very simple question: when you combine two sine waves with a phase shift between them, what is the output? It was relevant because this is essentially what is happening in a balanced mixer when it cancels intermodulation products. Simple, right? Voltage waveforms (not power) add vectorially, as [c2 = a2 + b2 + 2ab cos[theta]], convert back to dBm, finished. Bada bing bada boom, if not high school algebra than at least undergrad physics.
Breaking the laws of thermodynamics usually means that you’ve done something wrong. One of the things that I KNOW (the output power is equal to the input power, the peak voltages add vectorially, the output impedances are matched to the input impedances) must be wrong.
Generally it is best to use these principles to solve microwave and RF problems:
1) Conservation of power: Power in = Power out, all the time. If you can’t have more power and the extra has to go somewhere.
2) Impedance is constant: The impedance is the ‘boundary condition’ for the problem, defined by the geometry. Changing the impedance requires breaking Maxwell’s equations, not as bad as
The solution lies in the properties of a three port network. As shown in Microwave Engineering (Pozar, V.2, p. 353), a three port network cannot be both lossless, matched at all ports, and reciprocal. Thus the available three port devices are either non-reciprocal (circulator), lossy (resistive power divider), or unmatched (T-junction). The first doesn’t add power, so that’s out. I don’t have any resistors in my mixer, so this seems unlikely. The input and output impedances must not be matched. As detailed in the Mixer Basics Primer, the balance of a mixer comes from the cancellation of mixer products in the diode circuit, which makes it dramatically more difficult to analyze. Instead we will consider the case for Wilkinson Power Dividers. Resistive Power Dividers are a little different, but the math works out the same way if you just add 3 dB of loss. What happens is that at the point where the voltages combine the impedance is not actually 50 ohms, but is transformed by an impedance transformation. Below you’ll see the results of the experiment I did to confirm my formula.
The still puzzling part is where the power goes when the two vectors cancel each other. It is very similar to the creepy interference problem in optics, where you have two waves cancelling each other. In free space the power goes into the non-canceled lobes of the diffraction pattern. In a fiber interferometer the power is transferred into radiating modes that get absorbed by the cladding. Where, then, does the power go in an RF/microwave power combiner?