Stability in two-ports

[Abdeldjafer]

I wonder how an RF-choke and a bypass-capacitor can help improve stability?
Im trying to design an LNA using the BFP842ESD, they made an evaluation board, and in the component description they state that L1, C3 and L2,C4 is used both as RF-chokes, matching components and RF-input grounding, while L2,C4 is used as matching components, RF-choke and RF-decoupling.

I then decided to tune the RF-chokes and decoupling capacitors and the reason for that was to get a better understanding of how decoupling and RF-chokes works without much success, so my first question is how do the values of RF-choke and decoupling capacitor affect the RF-signal. And how do i choose an optimal value these components? The circuit is designed for 2.4GHz applications

When i tuned the components, the stability factor improved and i could obtain unconditional stability by only using tunning L2 and C4, in most cases resistive termination is used to obtain unconditional stability?

[szoftveres]

I have a hunch that R3 is part of the stabilization strategy. 6.8pf will not decouple all RF at 2.4GHz and some will end up on R3, essentially de-Q'ing the output tuned circuit, thereby providing stability. And if you change the reactive components, that will change the resonant impedance vs. R3 (Q factor), greatly impacting K.

[Abdeldjafer]

Thank you for the fast reply. I hope my question is clear

True R3 does help improve stability it is also stated in the application note, when you say "de-Q'ing the output tuned circuit" do you mean that lower resistance 
(in this case R3) in the output resonance circuit will improve stability?

The reason why i ask these questions is because i started my design with biasing and in this case i used ideal RF-chokes and DC-blocks. I want to choose values for RF-chokes and decoupling capacitors so they both work as RF-chokes and decoupling capacitors and in the mean time is a part of the matching circuit.

How should i choose RF-choke and decoupling capacitors?  Based on the definition of inductive and capacitive impedance i should choose a large capacitor and inductor and in this case the components will work as RF-choke and decoupling capacitor, if i have understood it correctly. But in the schematic i uploaded they don't use large values and i want to understand why?

[szoftveres]

Imagine that the common node of L2, C4 and R3 is the ground; in this case L2 and C2 form the output L-match. (Now, if you add C4 and R3, what you get is essentially an 'L-match on a lossy ground', i.e. the 'ground' node of the L-match is dissipating approximately 1/3 of RF through R3. This adds stability.)
The collector of the transistor is on the high impedance side of this L-match and consequently the 1.5pf output cap provides the 'tapped' lower impedance on its other side. So they hit three birds with one stone: matched the transistor to the output, while simultaneously decoupled DC with the 1.5pf capacitor and provided DC current to the collector via L2.

[EggertEnjoyer123]

The simple explanation is that oscillation occurs when you have too much gain compared to the reverse isolation (S12). If S21 is too high compared to S12, then you might have a situation where the signal gets amplified, then reflected from the output load, then attenuated through the isolation, then reflected back from the input load with higher amplitude, which causes oscillation.

The only way to increase stability is to waste power somehow to decrease the gain of the system. This is why only resistors can be used to improve stability. Changing the matching network is useless when it comes to improving stability (assuming the components are ideal) because ideal inductors and capacitors do not dissipate power.

In the circuit shown here, at low frequencies the resistor R3 affects the gain a lot. This is because the inductor looks like a short and the capacitor looks like an open, so power is dissipated in the resistor. At high frequencies, the capacitor dominates over the resistor since it basically shorts it out. This makes the resistor waste less power. The point of L2 and C4 is basically to decrease gain at low frequencies, and keep the gain relatively similar at higher frequencies. This is useful when the transistor is unstable at low frequency, but stable at high frequency. If you just used a resistor, then the gain would drop at all frequencies, but this circuit would keep the gain similar at high frequency while improving stability at low frequency.

Another useful trick is to put a resistor in series with a quarter wave transmission line and stub. At the frequency of interest, the quarter wave line and stub look like an open, so the circuit basically looks like a resistor with one end open. Therefore the gain is not affected at all at this frequency. At other frequencies, the stub and line no longer look like an open circuit, so the resistor will waste power and therefore stability would improve at all other frequencies.

[Abdeldjafer]

Thank you guys, good explanations.

[Abdeldjafer]

I have another question, now i use this configuration to achieve stability, i tuned the input matching circuit to achieve desired performance parameters. I simply use the RF-choke and DC-block together with C21 ( decoupling capacitor) to achieve the desired impedance at the input port.

Now, usually i pick a large inductor and a large capacitor to function as the choke and block, but in this example the inductor is 2.4nH and the DC blocker is 1.7pF. Can anyone give a short explanation to how this will practically work?

and each component has some parasitic capacitance and inductance, so each component has a frequency in which it will resonate, in relation to the SRF how should i choose each component.

As an example i can imagine that, choosing components for matching purposes should have the smallest deviation from its standard value, the problem here that each matching component, also functions as RF-chokes, coupling capacitors and DC-blockers.

[EggertEnjoyer123]

Since this is an LNA, you do not want any losses on the input side (since then your input power would effectively be less which would hurt your SNR).

Let's say you designed everything your way. It would look like the left side of the attached image. (Assume all unmarked components are large values). The 1.7pF and 2.4nH inductors are for matching, and the big capacitor and inductor are for DC biasing. At 2.4 GHz, the inductor looks like an open and the capacitor looks like a short. The right side shows the current circuit. At 2.4GHz the 160pF capacitor is very close to being a short. If you compare the left side and the right side with the red lines, you can see that they're equivalent at 2.4 GHz. The advantage is that the large inductor and capacitor aren't perfect in real life, and they also have loss. By eliminating those you can improve the efficiency of your matching network and get a lower noise figure.

In reality, the 160pF capacitor probably looks inductive at 2.4GHz. If the capacitor looked like a 0.6nH inductor, then you would have effectively 3nH inductance going to ground instead of 2.4nH. The resistor doesn't matter because the impedance of the 160pF capacitor is way smaller than it. So in reality, you might have to make the inductor smaller when you switch from the circuit on the left side to the right side.

I strongly suggest also simulating vias for every component lead going to ground. The via inductance absolutely matters at 2.4 GHz, unless you are using a 4 layer board. As for component choices the Coilcraft 0402DC is what I've used in previous designs.

[Abdeldjafer]

Understood, thank you for the explanation. What about the SRF of the components, what should i focus on when choosing each component?

What important parameters should i be careful about when choosing components. ?

[EggertEnjoyer123]

Ideally you would simulate everything in ADS, but try to get the highest quality factor at 2.4 GHz.

The Q for capacitors is usually pretty high, but not the Q for inductors.