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Hi, vfone, I have the same question regarding PA stability. You said K factor is for one stage amp. Is there a parameter to assess stability of cascaded amps by lab measurement??
Speaking from experience I can say that none of the existing stability factors (Rollett, Stern, Linvil) can help for multistage amplifier, from the simple reason that in a real life multistage amplifier appears problems that theory doesn’t take into consideration.
Rollett is based on S parameters which makes it accurate for single stage low signal amplifiers, when Stern is based on mismatching the source and load impedances at the expense of amplifier gain.
Just to give you an idea about potential instabilities of a multistage (but only for the first and the last stage), is to verify the S11 and S22 (low signal) to don’t be positive (or very close to zero). This doesn’t mean the amplifier it will oscillate at those frequencies, but could be just potential unstable (vs. input power, bias, load, etc)
Can these existing stability factors help for balanced amplifier?
What is the right approch to verify stability of multistage amplifiers, stage by stage stability factor? or checking output spectrum by sweeping frequency?
What is the right approach to verify stability of multistage amplifiers, stage by stage stability factor? or checking output spectrum by sweeping frequency?
I think, when you will attach 3 amplifers together, it will be a system, so when you will measure S paramters of these cascaded amplifiers, you will get the Stability measurement of the total system.
Individual satability consideration & system consideration are different.
ok, if you think of the entire 3-stage as a "single stage" and apply k-factor (or otherwise) and find out that this "single stage" is stable. does this guarantee that the three stage is stable?
all i can think of now is that if you guarantee that each stage is unconditionally stable then when you cascade them together it outage be stable (at least theoretically).
this is for unconditional stability. for conditional stability, I would guess that the theory is that if you make sure that each individually stage is conditionally stable (for all frequencies) and also the entire 3-stage cascaded one is also conditionally stable (for the same frequencies) then you can probably say that the entir 3-stage is conditionally stable for those frequencies. but the problem is that conditional stability is impedance-frequency dependent and to test if an individual stage is conditionally stable is very difficult because you have to mimic its source and load impedance (which are from its previous and next stage and they themselves are dependent on its previous or later stage) for that stage.
this is why i have the question at the begging: if you simply have conditional stability for the entire 3-stage (regarded as a single stage) does this mean that it is conditionally stable for the entire 3-stage? my thought is: not necessary because for example, what if the first stage and last stage are completely isolated from the middle stage and therefore the overall 3-stage looks stable of course but in fact the middle one might just be unstable. of course, this is an extreme condition...
so did anyone see any literature investigating the conditional stability of cascaded stages? or maybe the answer to my question at the beginning is simply yes (i.e. if the entire 3-stage is conditionally stable then the it is conditionally stable-simple as that, at least theoretically).
Finally somewhere this is discussed. I have been trying to find out if theory can be applied for more than one amplifier stage, but from what I've read, none of the existing theoretical approaches (Rollets, or mu-stability) can be applied for a cascade. Although, I was told by a PhD student that "just compute the stability factors for the entire cascade. It should work"... I don't know if I believe that.
I am using three LNA's in cascade. All are of the same type, the amplifier is by itself unconditionally stable at least for the range 1 - 7 GHz. It is designed for a center frequency of 3.5 GHz, and within the bandwidth at least, it is faaar from unstable.
The problem is, as experience have taught me, that if you cascade three of these amplifiers, you have made an oscillator. If you cascade two, they are stable. So what happens? It could be that the increased gain just tips the whole thing over .. It could be that at the last stage, enough power is reflected back and forth again that oscillation will occur. I dont know. Could also be because the dimensions between them are so small that there is a feedback through their radiated fields.. So, I have used an isolator between the last two LNAs to decouple them. Now the cascade is stable. BUT! How can I theoretically support this? I only have CST at hand. And I can only simulate the devices using S-parameters. But seemingly, I cannot compute the stability parameter for the simulated S-parameters of all three in cascade. And likewise, I cannot compute it when I simulate the same with an isolator between them.
If it is an LDMOS PA I assume you will be driving it into the non linear region so I'm not sure that playing with small signal s parameters is ever going to give you anything conclusive.
You are more likely to get very low frequency oscillations if you don't have a well controlled bias network or a feedback path that isn't modelled by simple S parameters. eg there could be mutual coupling between inductors or reflections from the output back to the input via the lid of an enclosure. Sometimes with large signals LDMOS will oscillate at a certain drive frequency and certain drive level only. This is due to dynamic changes in the device that can't be modelled using small signal s parameters. Also, it will be more likely to oscillate at colder temperatures.
The best advice I can give wrt an LDMOS PA is to look very carefully at the gate bias components and make sure that the gate bias is held 'stiff' with a low impedance at low (eg audio) frequencies.
Also, put a tracking generator though the PA stage and look for peaking out of band because you can sometimes introduce problems if the PCB and the device aren't grounded as well as you might think they are. This can lead to instability out of band and this is hard to model so you really have to go and look for signs of it.
Hi, panchoo. I re-posted my problem in the forum you qoute. I you have time to look at it, and perhaps discuss this problem with me, i would love you for it.
For a single stage ampifiers the stability factors (k, mu) give accurate results. Critera of stability is based on the assumption that input and output loads are passive (moduo of reflection less than 1). When cascading amplifier stages, one transistor becomes loaded with the other one, therefore there is no longer garantee that loads are passive (i.e. moduo of reflection is not restricted to be less then 1). In such a circumstances it is very difficult to ensure stability. In AWR I thing there is some kind of circulator-like probe to put between the stages to sense the stability breaches in multistage environment, think this is a practical way to deal with the problem, not sure it found a ground in some theory.
I agree with you. K factor does not suitable for multi-stage "Power Amplifer" nor "Single Stage" neither. Because PA always operate in non-linear region. It means the bias is always changing varies with time. We can use linear and small signal s parameter to predict the non-linear device behavior. But I saw a paper that we can measure the extreme bias condition s parameter and calculate the k factor to check the circuit stability.
As GOHZU said that PA will oscillate in specific input power, frequency and load impedance at low frequency. It is true because I am suffering this problem now:sad:. I am searching the parameter or method to measure why the circuit will be unstable for a long time. But I still can not find it.
Recently I see Agilent provide a new measured parameter "X parameter" as like s parameter, but it is non-linear.
I don't know it can be apply in non-linear stability issue or not. You can google it maybe you will get some inspiration from it.
If it is an LDMOS PA I assume you will be driving it into the non linear region so I'm not sure that playing with small signal s parameters is ever going to give you anything conclusive.
You are more likely to get very low frequency oscillations if you don't have a well controlled bias network or a feedback path that isn't modelled by simple S parameters. eg there could be mutual coupling between inductors or reflections from the output back to the input via the lid of an enclosure. Sometimes with large signals LDMOS will oscillate at a certain drive frequency and certain drive level only. This is due to dynamic changes in the device that can't be modelled using small signal s parameters. Also, it will be more likely to oscillate at colder temperatures.
The best advice I can give wrt an LDMOS PA is to look very carefully at the gate bias components and make sure that the gate bias is held 'stiff' with a low impedance at low (eg audio) frequencies.
Also, put a tracking generator though the PA stage and look for peaking out of band because you can sometimes introduce problems if the PCB and the device aren't grounded as well as you might think they are. This can lead to instability out of band and this is hard to model so you really have to go and look for signs of it.
Anyway, K factor is not sufficient to ensure stability.
I m afraid that anybody mentioned NDF (normalized determinant function). For multistage power amplifier an accurate analysis technique is called NDF. Thid method has been published everywhere, try to google it.
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. But I still can not find it.