Low-noise amplifiers (LNAs) form the input stage of the receiving part of nearly any communications system. The main task of these subcircuits is to amplify the wanted signal without deteriorating the signal-to-noise ratio. In most cases, the desired signal is very weak. The noise figure is seen as the main describing figure of merit for the transistors used in such applications. It determines the minimum amount of noise that is added in the transistor stage. The noise figure is not a hard figure, as it depends on the bias and especially the input matching conditions.

According to many microwave textbooks, nothing is easier than the design of a matching network for a specific transistor. The engineer simply needs to know the S-and noise parameters at an appropriate bias point for that transistor. Yet a design problem might arise if stability is a concern. The noise match is routinely done by setting the input noise and output gain match, which is a standard procedure in many textbooks (e.g., Ref. 1, Ch. 4.1.2). There is not much room to influence or even improve the stability factor. As a result, stability is often checked only after the design is completed.

The "traditional" way of making a noise match is repeated here. For a given transistor, a set of S-and noise parameters, S_nm and N, is available at the bias point of interest. The noise match, τ_M [the index M stands for Minimum (Noise)], is taken from the set of noise parameters, N, at the operating frequency. The load match, τ_L (index L means Load), is then calculated for maximum gain. With this procedure, the question of stability is ignored. It can only be checked after the τ_L is determined. With a general τ_S (index S means Source, presented to the input of the transistor), the noise figure, F, is calculated as:

where r_n = R_n/Z₀. Note that Z₀ is the characteristic impedance of the transistor (in most cases, 50 Ω). Two points should be emphasized at this stage:

• As can be seen from Eq. 1, only the input impedance τ_S determines the noise figure, F, from an application point of view. F_MIN, r_n, and τ_M are characteristics of the transistor in the selected bias point. To get the minimum noise figure available, F_MIN, τ_S should be set to T_M.
• F is not affected by the load impedance, τ_L

The stability of a given transistor is mostly described by the K-factor, which is computed as follows:

Because many textbooks explain why K > 1 means unconditional stability, that information is not repeated here (see Ref. 2 or Ref. 3 for further explanation). With the procedure described, it is helpful if the transistor is unconditionally stable at any frequency. Unfortunately, this is not the case for many devices. In a lot of applications, the circuit designer is choosing the transistor according to parameters presented on its datasheet, such as available gain, third-order intercept point (IP3), operating voltage, F_MIN, and others. The last step is to check the transistor's Sparameters for stability. In the design stage, it may be found that the transistor tends to oscillation. This knowledge is especially damaging when gained at the production stage.

Fortunately, it is possible to " stabilize" a transistor when the LNA is designed. The overall rule is to decrease the gain of the entire LNA. This approach will help to increase the K-factor and thus stabilize the LNA. From a circuitdesign point of view, the following possibilities exist:

• Mismatch the output. This approach will decrease the stage's gain and improve the stability. But it also may lead to matching problems regarding the following LNA stage. In addition, S22 may be deteriorated. Looking at the numerator of Eq. 2, it is clear that this approach may not really help to increase the K-factor.
• Introduce some amount of resistive feedback. In a common emitter/source circuit, feedback is applied between the base/gate and collector/drain. In most cases, a capacitor also will be needed to block the different DC levels from each other. Because this method also is changing the input parameters, significant changes in the noise parameters need some modifications.
• Load the output (collector/drain) resistively to ground. Many advantages come with this technique. The gain is reduced for some amount and S22 is improved if the resistive loading is made in a proper region. These two effects work in a common direction to improve the K-factor. In addition, this technique can be easily incorporated in the output biasing circuit.

The starting point of the last technique is an s2p-file of a model NE661M04 transistor from NEC/ California Eastern Laboratories (www.cel.com) in Touchstone file format including the noise parameters. The device for this example is a silicon-bipolar transistor that provides unconditional stability in the LNA design that is presented.

To design the LNA, the target specifications must first be defined. Because this example should show the stabilizing part of the design phase, only the small-signal, linear specifications are given here:

• Frequency: 2 GHz (narrowband design)
• Gain (S21): >16 dB
• Noise figure: <1.7 dB
• Stability: unconditionally stable (K>1 for all frequencies)

Compared to the design center frequency, an initial check of the S-parameters in the first step shows that the Kfactor remains less than unity at higher frequencies. In this case, the transistor would remain unstable with the normal procedure by just setting a noise match at the input and a gain match at the output. The ADS linear testbench and data display are shown in Fig. 1 and Fig. 2, respectively.

In the data display, the four S-parameters are given versus the frequency accompanied by the noise figure and K-factor (lower right display). The K-factor stays below unity through approximately 2.5 GHz and therefore also at the intended operating frequency at 2 GHz. The transistor's behavior is potentially unstable.

Such behavior may lead to problems in the LNA. If this LNA is the first amplifier in the signal chain connected to the antenna, its input impedance may be affected by the load imposed by the antenna. Such effects as tuning or degrading the antenna by touching small mobile phones with the user's hand or snow on an LNB horn may affect the LNA's source impedance. Of course, the impedance can be checked with the method of stability circles. If the LNA is not unconditionally stable at all frequencies, however, these ambient interactions will not just degrade the noise figure. They also can start transistor oscillations that may shift the bias point ( mostly to higher current consumption) or even destroy the transistor. Checking the stability of an LNA is thus a kind of quality issue for the entire product.