[SOLVED] How to Address Matching Issues of T-Junctions in Amplifier Design:

[Shawn Jobs]

As a three-port device, a T-junction cannot simultaneously achieve matching, reciprocity, and losslessness. My question is: If an amplifier is connected after the T-junction, and Port 1 is already matched, how can we achieve conjugate matching at Ports 2 and 3 for the amplifier input? Is this even feasible?

 

[mtwieg]

Why would the presence of a splitter prevent conjugate matching?

If an amplifier is connected after the T-junction, and Port 1 is already matched

What do you mean by "port 1 is already matched"? You mean matched when ports 2 and 3 are terminated by something other than the amplifiers, like Z0?

In the simple case that amplifiers are identical, then matching can be approached normally, each with an identical matching network between its input and the splitter output. Or you could connect the amplifiers directly to the splitter and put a single matching network on the input to the splitter.

 

[Shawn Jobs]

Why would the presence of a splitter prevent conjugate matching?

What do you mean by "port 1 is already matched"? You mean matched when ports 2 and 3 are terminated by something other than the amplifiers, like Z0?

In the simple case that amplifiers are identical, then matching can be approached normally, each with an identical matching network between its input and the splitter output. Or you could connect the amplifiers directly to the splitter and put a single matching network on the input to the splitter.

Thank you for your reply. What I meant was: Assuming Port 1 is already matched, I want to configure the T-junction’s Port 2 and Port 3 for conjugate matching with the subsequent amplifier inputs. As you described in the first scenario, if this is achieved, does it imply that all three ports are now fully matched? If so, wouldn’t this contradict the theoretical limitation (that a three-port passive device cannot simultaneously satisfy matching, reciprocity, and losslessness)? I’m a bit confused about this.

 

[mtwieg]

What I meant was: Assuming Port 1 is already matched

I'm guessing you mean that S11 of port 1 of the junction is near zero? Not that gamma looking into that port is near zero.

I want to configure the T-junction’s Port 2 and Port 3 for conjugate matching with the subsequent amplifier inputs. As you described in the first scenario, if this is achieved, does it imply that all three ports are now fully matched?

One of the fundamental properties of a lossless, reciprocal two port network is that if one side sees a conjugate match, then the other side is also conjugate matched. We can't extend this to three port networks though, it's entirely possible for two ports to be conjugate matched but not the third. But there is definitely nothing forbidding all three ports from being conjugate matched.

Again, a trivial example is a splitter being terminated with Z0 on all ports. All ports are conjugate matched. Now replace the Z0 termination on ports two and three with amplifiers with impedance transformers that present their inputs as being Z0. All ports are still conjugate matched (at least at one frequency, that is).

 

[BigBoss]

First, amplifiers cannot be connected in this way because each amplifier impacts the other one so this is a really constrained/troublesome configuration.
Instead, Wilkinson Power Divider was innovated for power division or combining to improve isolation between amplifiers.
Conjugate Matching is not in reality desired specification because Wilkinson Power Divider/Combiner has already matched to characteristic impedance.

 

[mtwieg]

I was assuming they were referring to something like a wilkinson splitter (otherwise referring to it as "matched" makes no sense).

If the intent is to also combine the amplifier outputs then a balanced amplifier using hybrid couplers is usually a better approach.

 

[Shawn Jobs]

I'm guessing you mean that S11 of port 1 of the junction is near zero? Not that gamma looking into that port is near zero.

One of the fundamental properties of a lossless, reciprocal two port network is that if one side sees a conjugate match, then the other side is also conjugate matched. We can't extend this to three port networks though, it's entirely possible for two ports to be conjugate matched but not the third. But there is definitely nothing forbidding all three ports from being conjugate matched.

Again, a trivial example is a splitter being terminated with Z0 on all ports. All ports are conjugate matched. Now replace the Z0 termination on ports two and three with amplifiers with impedance transformers that present their inputs as being Z0. All ports are still conjugate matched (at least at one frequency, that is).

First, amplifiers cannot be connected in this way because each amplifier impacts the other one so this is a really constrained/troublesome configuration.
Instead, Wilkinson Power Divider was innovated for power division or combining to improve isolation between amplifiers.
Conjugate Matching is not in reality desired specification because Wilkinson Power Divider/Combiner has already matched to characteristic impedance.

Thank you both for your responses. Let me briefly describe the issue I'm facing. For example, when I design a T-junction with all three ports set to 50 ohms, the results show good S11 matching at Port 1, but poor matching at Ports 2 and 3 (which aligns with conventional expectations). However, if I want to match Ports 2 and 3 to a specific impedance value (e.g., 15-j15), how should I proceed? In Figure 2, I added two components to transform the (15-j15) impedance to 50 ohms(Characteristic impedance), but according to the simulation, the input impedances seen at Ports 2 and 3 still do not reach the desired values. Is this an inherent limitation of the T-junction structure?

 

[mtwieg]

Thank you both for your responses. Let me briefly describe the issue I'm facing. For example, when I design a T-junction with all three ports set to 50 ohms, the results show good S11 matching at Port 1, but poor matching at Ports 2 and 3 (which aligns with conventional expectations).

Not sure why you say this aligns with conventional expectations (certainly would not be the case with a dead short circuit), as you still haven't defined clearly what this T-junction actually is. Looks like you've defined three Z0 values for it, but no lengths.... could you just share the S parameters of this T-junction? I don't have access to ADS.

However, if I want to match Ports 2 and 3 to a specific impedance value (e.g., 15-j15), how should I proceed? In Figure 2, I added two components to transform the (15-j15) impedance to 50 ohms(Characteristic impedance), but according to the simulation, the input impedances seen at Ports 2 and 3 still do not reach the desired values. Is this an inherent limitation of the T-junction structure?

What I see is that S11/S22/S33 have all changed phase, but not magnitude, as expected for adding lossless impedance transformers to the ports.

 

[Shawn Jobs]

Not sure why you say this aligns with conventional expectations (certainly would not be the case with a dead short circuit), as you still haven't defined clearly what this T-junction actually is. Looks like you've defined three Z0 values for it, but no lengths.... could you just share the S parameters of this T-junction? I don't have access to ADS.

What I see is that S11/S22/S33 have all changed phase, but not magnitude, as expected for adding lossless impedance transformers to the ports.

Thank you for your patient explanation. Figure 1 presents the S-parameters of the designed T-junction (with all three ports designed for a characteristic impedance of 50 ohms), and its internal structure is illustrated in the figure below.

 

[mtwieg]

Ok clearly I was misunderstanding, I was assuming your "junction" was some sort of splitter with decently isolated ports (like a wilkinson splitter). If you're actually referring to a literal T with no isolation at all, then yes it is impossible for all three ports to see a conjugate match at the same time.

Is there some reason you can't use a conventional splitter? Is matching at all ports actually important?

 

[Shawn Jobs]

Ok clearly I was misunderstanding, I was assuming your "junction" was some sort of splitter with decently isolated ports (like a wilkinson splitter). If you're actually referring to a literal T with no isolation at all, then yes it is impossible for all three ports to see a conjugate match at the same time.

Is there some reason you can't use a conventional splitter? Is matching at all ports actually important?

Thanks again for your detailed answer—it completely cleared up my confusion. Proper isolation is essential to maintain matching across all three ports