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@Stealthflanker
OK, I see. The +29dB gain was the outcome of your own calculation.

Well, I have to question your results.

1. Baseline SPY-1 range: 281km against a 2m2 target. What's your source for this?
The only public numerical figure on the SPY-1 radar detection range against a specific target is that the it“can track golf ball-sized targets at ranges in excess of 165 kilometers.” A golf ball-size (1.68 inches diameter) metallic sphere corresponds to radar cross section of about 0.0025 m2 at 3.3 GHz. These figures are presumably for the SPY-1D(V) variant. Source: John A. Robinson, “Force Protection from the Sea: Employing the SPY-1D Radar,” Field Artillery, March-June 2004, pp. 24-25.

2. You used 58kW as average power for the SPY-1 radar.
I see two problems with this. The SPY-1D radar does not emit simultaneously from all 4 faces. It timeshares the same transmitter over the 4 faces, therefore you need to divide the power by 4. The SPY-1B radar on the Aegis cruisers has two transmitters, so you need to divide by 2. Secondly, the SPY-1D(V) came with a 33% increase in duty cycle or 77kW average power assuming that SPY-1D was 58kW. This source has some interesting estimates for the SPY-1D(V) radar:
Finally, these numbers may be power at the transmitter and not emitted power. To quote mostlymissiledefense:

According to a 2004 Defense Science Board Report, “the average radiated power aperture for the Aegis System is 485 kwm2.”

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Assuming that statement applies to the SPY-1D (since the SPY-1D(V) version was not yet operational) and an antenna area of 12 m2, this would give an average emitted power of about 40 kW.

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3. You set the SPY-1 antenna area as 13.3m2
This is too high. While there is no official number on the aperture area, reputable sources put it around 12m2. This source is replete with useful data:

Otherwise i wonder how do you make your conclusion about "100 times more sensitive" ?

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That's not my conclusion. The source for that is Mike Mills, Raytheon's SPY-6 program director
You can read about it here:

SPY-1D(V) was estimated to have a detection range (S/N=20) of 550km against a target with a RCS of 0.03m2 in S-band. This was done for a ballistic missile defence fence search, where the radar channels all its transmitter power through a single radar face. The author described this as an "overestimation" because the SPY-1 radar is unlikely to afford 0.1s long dwells in normal operating conditions.

Zichan said:

OK, I see. The +29dB gain was the outcome of your own calculation.

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So are you going to make comparable calculations ? Now you cannot say that Loop gain is not a merit used by the US. Now i am asking you how do you define the "sensitivity".

Zichan said:

Well, I have to question your results.

1. Baseline SPY-1 range: 281km against a 2m2 target. What's your source for this?
The only public numerical figure on the SPY-1 radar detection range against a specific target is that the it“can track golf ball-sized targets at ranges in excess of 165 kilometers.” A golf ball-size (1.68 inches diameter) metallic sphere corresponds to radar cross section of about 0.0025 m2 at 3.3 GHz. These figures are presumably for the SPY-1D(V) variant. Source: John A. Robinson, “Force Protection from the Sea: Employing the SPY-1D Radar,” Field Artillery, March-June 2004, pp. 24-25.

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They are also my calculations too based on the available data i am also used Norman Friedman's book. I do not use that 165 km range because it does not specify the condition of the measurements. For SNR i use 24 dB as that's what needed for a Swerling 1 Target.

Naturally tho i expect it would be different as others may use different values especially SNR. For SNR or Do (Detectability Factor) I use K.Barton's Radar equations.

Zichan said:

2. You used 58kW as average power for the SPY-1 radar.
I see two problems with this. The SPY-1D radar does not emit simultaneously from all 4 faces. It timeshares the same transmitter over the 4 faces, therefore you need to divide the power by 4. Secondly, the 58kW figure is for the SPY-1B radar. The SPY-1D(V) came with a 33% increase in duty cycle or 77kW average power. This source has some interesting estimates for the SPY-1D(V) radar:

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I only assume 1 face tho, and 1% duty cycle based on the available information for pulsewidth. and even it does not emit from all 4 faces at same time i am not sure If one needs to divide it by four. So the average power be it 58 or 77 KW It is emitted by the 1 face.

Zichan said:

That's not my conclusion. The source for that is Mike Mills, Raytheon's SPY-6 program director
You can read about it here:

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So you dont try to find further what do they mean by sensitivity ? Because i find it and it's kinda not what i expected when i discovered loop gain.

Now. i need to add particularly on the Beauty of using Loop Gain is that... It's consistent

Regardless your range figure. As long as your target model is consistent (consistent Target RCS), SNR and with your range figure. You can practically extrapolate the result.

Zichan said:

SPY-1D(V) was estimated to have a detection range (S/N=20) of 550km against a target with a RCS of 0.03m2 in S-band. This was done for a ballistic missile defence fence search, where the radar channels all its transmitter power through a single radar face. The author described this as an "overestimation" because the SPY-1 radar is unlikely to afford 0.1s long dwells in normal operating conditions.

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Now if we use that value (the SNR of 13 dB, 0.03 sqm RCS and predicted range of 550 km) To calculate the loop gain of the SPY-1D(V) You will find baseline loop-gain for SPY-1D mentioned in the article as 258 dB.

Repeating the same calculations for AMDR performance sheet i made yield this.



Notice the loop gain improvement value. They're Still the same 29 dB for 82 RMA Radar vs Baseline SPY-1.

I see that it is not productive for me to try and dispute the range estimate result as it may produce same result for Loop gain and therefore definition of sensitivity. It is actually an elegant way to say performance improvement without divulging potentially secret information such as actual test results or others.

Stealthflanker said:

So are you going to make comparable calculations ? Now you cannot say that Loop gain is not a merit used by the US. Now i am asking you how do you define the "sensitivity".

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I think you are probably on the right track with the "loop gain". I looked at the definition and it matches my expectation of "sensitivity".

Stealthflanker said:

I only assume 1 face tho, and 1% duty cycle based on the available information for pulsewidth. and even it does not emit from all 4 faces at same time i am not sure If one needs to divide it by four. So the average power be it 58 or 77 KW It is emitted by the 1 face.

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The problem is here is that you are not making an apples to apples comparison. A PESA radar like SPY-1D has a central amplifier that has to be shared across 4 faces.

An AESA radar, however, has amplifiers as part of the radar faces. Therefore, modern AESA radars can emit simultaneously from all 4 faces at full power (unless the power source is under specced for some reason). Constraining a 4 face AESA radar to use just 1 face is not a fair comparison IMO.

Furthermore, AESA radars tend to have smaller system losses than PESA radars: no complex waveguides and high power through the phase shifters resulting in lower system noise temperature and lines losses. Not sure if you took this into account? Can you share the parameters that you used for the SPY-6 radar?

Zichan said:

The problem is here is that you are not making an apples to apples comparison. A PESA radar like SPY-1D has a central amplifier that has to be shared across 4 faces.

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and if you use Loop gain as measure it wont care whether your radar is AESA or PESA. 0 dB of improvements is basically your AESA and PESA have same value of Loop gain.

Zichan said:

Can you share the parameters that you used for the SPY-7 radar?

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Well i assume this is similar as the SPY-6. because both types of Radar are said to be Scaleable i think they will share same RMA architecture and very similar in performance. Therefore i assume it will be just like SPY-6 but with 82 RMA Instead of 69 the biggest of What Raytheon offers.

Stealthflanker said:

and if you use Loop gain as measure it wont care whether your radar is AESA or PESA. 0 dB of improvements is basically your AESA and PESA have same value of Loop gain.

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I asked because in the secret projects forum you used the SPY-1 power to determine the AMDR power:

First is of course we would need to find the power of the AMDR. The 9 RMA variant offers 0 dB means it will be equivalent to baseline SPY-1. This indicates it would have similar emitted power. One can assume it would have exactly 58 KW of average power. With each RMA contain about 144 TRM's this will indicate that the 9 RMA variant would have 1296 TRM in total, where each TRM will shoulder about 58/1296 = 45 Watt of average power.

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Because of the caveat above, this is going to be significantly off the mark.

However, I have some reservations about the 58kW or the 77 kW figure. The input power to the SPY-1D radar is on the order of 1MW. The CFA amplifiers as used in the SPY-1 radar can have efficiency up to 70%. Even including the line losses, phase shifter losses and power conversion losses, a 7.7% efficiency still strikes me as unusually low.


EDIT: I should also point out that SPY-1 can emit pulses longer than 6.4us. According to Friedman, the upper range on pulse width is 51us. I expect you are using dwell time and not pulse width time? AESA radars tend to have much longer pulses than PESA radars (because of much lower peak power)

Zichan said:

EDIT: I should also point out that SPY-1 can emit pulses longer than 6.4us. According to Friedman, the upper range on pulse width is 51us. I expect you are using dwell time and not pulse width time? AESA radars tend to have much longer pulses than PESA radars (because of much lower peak power)

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I am using dwell time. You can even use both Dwell time and pulsewidth but that case is for Non-coherent radar. For coherent radar i use dwell time and this i assume to be 0.025 seconds. It is not in the table at first but it's there That pulsewidth is there for example case and i also put my data in that sheet.

The thing is that you can compensate low peak power by :
1.Longer pulsewidth as you mentioned
2. Increased PRF

Those two will drive up your duty cycle and in turn drive up your Average power. So you can still get that 77 or 58 KW average with 6.4 us pulsewidth.

Zichan said:

Because of the caveat above, this is going to be significantly off the mark.

However, I have some reservations about the 58kW or the 77 kW figure. The input power to the SPY-1D radar is on the order of 1MW. The CFA amplifiers as used in the SPY-1 radar can have efficiency up to 70%. Even including the line losses, phase shifter losses and power conversion losses, a 7.7% efficiency still strikes me as unusually low.

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and who is making the mark ? and significant here requires real statistics. Also what kind of accuracy you actually expect from the calculation tho ?

I wonder what is your example of "high" efficiency radar.

Zichan said:

I asked because in the secret projects forum you used the SPY-1 power to determine the AMDR power:

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and Raytheon used it as baseline to compare AESA AMDR. Thus i feel it's reasonable to start from there.

Stealthflanker said:

and who is making the mark ? and significant here requires real statistics. Also what kind of accuracy you actually expect from the calculation tho ?

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I am just trying to help you. Attempting to derive the AMDR TRM power based off the SPY-1 power strikes me as the wrong way to go about here and not just for the fact that their total radiated power across a hemisphere is going to be different from what you assumed.

Zichan said:

I am just trying to help you. Attempting to derive the AMDR TRM power based off the SPY-1 power strikes me as the wrong way to go about here and not just for the fact that their total radiated power across a hemisphere is going to be different from what you assumed.

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So it's no longer about range, loop gain and now it's about power. At this point tho the real help is you yourself have to demonstrate your skill instead of quoting sources. start step by step of calculations, show the proper calculation methods. Calculate the Loop Gain.. and if it ended up the same way as my result i wonder what's next.

Now i wonder how will you try to estimate the AMDR TRM power ? Like i'm kinda feel 58 or 77 KW is a good and reasonable start.

any less or any-more will require information about generating capacity and cooling capacity available in the ship. Cooling is especially important if you want to backfit it to the older ships. Any more emitted power requires Heavier and maybe Bulkier cooler.

Stealthflanker said:

So it's no longer about range, loop gain and now it's about power. At this point tho the real help is you yourself have to demonstrate your skill instead of quoting sources. start step by step of calculations, show the proper calculation methods. Calculate the Loop Gain.. and if it ended up the same way as my result i wonder what's next.

Now i wonder how will you try to estimate the AMDR TRM power ? Like i'm kinda feel 58 or 77 KW is a good and reasonable start.

any less or any-more will require information about generating capacity and cooling capacity available in the ship. Cooling is especially important if you want to backfit it to the older ships. Any more emitted power requires Heavier and maybe Bulkier cooler.

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There’s more parameters than just power. I pointed out earlier that your aperture size for SPY-1 was wrong, hence also the antenna gain. Furthermore, we don’t know the system noise temperature and line losses for SPY-6.

To estimate the SPY-6 TRM power, we can survey state-of-the-art GaN S-band HPAs to get an idea what the range of plausibility is. I think @Tam has done good work on that field.

Although to come back to my original point:
The SPY-1D(V) “can track golf ball-sized targets at ranges in excess of 165 kilometers.” A golf ball-size (1.68 inches diameter) metallic sphere corresponds to radar cross section of about 0.0025 m2 at 3.3 GHz.

My argument: even without knowing SPY-1s loop gain, the fact that the 37 RMA SPY-6 is +20dB (100x) more sensitive (loop gain) allows us to determine the range at which it can track the golf ball at the same (uknown) SNR.

r_spy6= 100^(1/4) * 165 = 759km.

We can also estimate performance against other RCS targets (for the same unknown SNR).

That’s based on my assumption that the loop gain difference between SPY-1 and SPY-6 remains constant, regardless of SNR and target cross section. Does that hold or not?