Active and Diversity Receiving Antenna Systems
3.3 Low Noise Amplifier Parameters .1 introduction.1 introduction
External electrical devices (including car electronic component noise
•
sources) Itself
•
The antenna noise temperature is an important factor that determines the minimal level detectable by the receiver signal. The antenna noise tempera-ture TA [3, pp. 99] is given by:
TA= + ⋅T Ta p −
1 1
η2 (3.18)
where Ta = noise temperature contributions from external sources, Tp = physi-cal antenna temperature (generally T0 ≈ 290 K), and h2 = thermal efficiency of the antenna. The operating noise temperature of the receiving system with an active antenna can be expressed as Tsys = TA + Tamp + Tr/Gamp where Tr is the noise temperature of a car receiver with an RF cable.
3.3 Low Noise Amplifier Parameters 3.3.1 introduction
The main parameters of a low noise amplifier are power gain, input and out-put impedances, noise figure, amplifier stability, frequency bandwidth, 1 dB compression power point level, and intermodulation distortion. An LNA design presents considerable challenge due to its simultaneous requirements for high gain, low noise, good input and output matching, and unconditional stability at the lowest possible current draw from the amplifier.
Transistor selection is the first and the most important step when designing an LNA. If the antenna has very low radiation resistance (less than a few ohms), imped-ance matching of antenna and amplifier input is difficult. In this case, a transistor with very high input impedance is used and provides the maximum transmission voltage value from antenna to receiver and a reasonable noise output value.
3.3.2 S Parameters
Typically, scattering (S) parameters ([4], pp. 23 and 24) are used by elec-tronic engineers to describe main amplifier characteristics such as gain,
input and output impedance, and VSWR. Every transistor or amplifier cir-cuit can be characterized for any specific operation frequency point by four complex S-parameters:
S
• 11 or input port voltage reflection coefficient S
• 21 or forward voltage gain S
• 12 or reverse voltage gain S
• 22 or output port voltage reflection coefficient 3.3.3 Stability Analysis
Stability analysis should be the first priority when designing an LNA.
Unconditional stability is the goal: for any load presented to the input or output of a device, the circuit will not become unstable (will not oscillate).
Instabilities are primarily caused by three phenomena: internal feedback of the transistor, external feedback around the transistor caused by an exter-nal circuit, and excess gain at frequencies outside the band of operation. S transistor parameters generally provided by the manufacturer will aid in stability analysis of the LNA circuit. The main technique in S parameter sta-bility analysis involves calculating a term called the Rollett stasta-bility factor K (Reference [4], pp. 217–223]). To estimate the final equation for the K factor, an intermittent quantity called delta Δ should be calculated first:
∆ =S S11⋅ 22−S S21⋅ 12 (3.19)
When the K factor is greater than unity and |Δ| < 1, a circuit will be uncondi-tionally stable for any source and load impedance value. When K is less than unity, the circuit is potentially unstable and oscillation may occur with a cer-tain combination of source and/or load impedance presented to the transis-tor. A sweeping of K factor over the wide frequency band for a given bia.sing point has to be performed to ensure unconditional stability outside the band of operation. The goal is an LNA circuit that is unconditionally stable for the complete range of frequencies at which the device has a substantial gain.
3.3.4 Amplifier gain
The S parameters of a transistor help in designing a matching system that transfers maximum power from an antenna to a receiver. Two different matching methods are applied to a transistor: one provides the maximum
gain of the amplifier system and the other provides the minimum noise that the transistor brings to the receiver.
To aid in finding a matching solution that maximizes amplifier gain, let us examine Figure 3.2, a block diagram with the following elements: an antenna as a power source with impedance Za (for example, Za = 50 ohm), an input matching circuit, a transistor with S parameters, output matching circuit, RF cable, and car receiver (for example, a 50 ohm cable with a 50 ohm receiver).
The reflection coefficient ΓIN is an input to the transistor, ΓOUT is the output reflection coefficient, Γs is the source reflection coefficient seen from the out-put side of the inout-put matching circuit, and ΓL is the load reflection coefficient seen from the input side of the output matching circuit. Impedance values ZS, ZIN, ZOUT, and ZL are related to the corresponding reflection coefficients in a Z0 system with the following simple expression:
Γi i
Let us assume that the amplifier in Figure 3.2 does not have input and output matching circuits (ΓS = 0, ΓL =0). The gain of the amplifier, called the trans-ducer power gain, is equal to:
G Power delivered to the load Power available fro
shown in Figure 3.2, the input and output reflection coefficients can be expressed ([4], p. 214) as:
Γ Γ from the output side of the input matching circuit and ΓL is the load reflec-tion coefficient seen from the input side of the output matching circuit. The gain value (3.21) in this case is given by the following
G S
3.3.5 Matching for Maximum Amplifier gain
To maximize the gain of the amplifier system (transistor + input matching circuit + output matching circuit), the matching circuit design must meet certain conditions ([4], pp. 240 and 241):
ΓS=Γin* ; ΓL=Γout* (3.25) This conjugate matching provides maximum gain, determined by:
G S
S K K
TMAX=| || |2112 ⋅
(
− 2−1)
(3.26)This equation assumes that the amplifier is unconditionally stable (K > 1 and
|Δ| < 1). If S12 ≈ 0, we have a so-called unilateral network (S12 is small enough and ignored), and the formula for the gain value is modified ([4], p. 228) as follows:
Optimized values ΓS and ΓL to provide maximum gain are given by:
ΓS S ΓL S GTU
A number of computer programs can help find the values of reflection coef-ficients ΓS and ΓL to a certain Pmax. One powerful program is Genesys from Eagleware Corporation [5].
As an example, let us choose a transistor with the following complex S parameters at 200 MHz frequency: S11 = 0.92/–29; S21 = 1.39/154; S12 = 0.002/72; and S22 = 0.97/–11. S parameters are expressed in magnitude and phase values. The results of computer simulations are the following: Gmax = 23.5 dB, K = 1.7 (transistor is unconditionally stable); ΓS = 0.932/31.8; and ΓL = 0.975/12.
Figure 3.3 presents a matching circuit tuned for maximum power (con-jugate) matching for the transistor parameter example. The basic equations (3.22) to (3.28) and simulation results show how to find a solution that pro-vides the maximum power delivered from the source to the load using an amplifier with matching circuits, but this solution does not provide minimal noise value at the amplifier output.
3.3.6 Noise Matching Design
A typical approach in LNA design is to devise an input matching circuit that terminates the transistor with a reflection coefficient, ΓS = Γopt representing the optimum terminating impedance of the transistor for the best noise match (see Reference [4], pp. 234 and 235). In many cases, this means an optimum noise match with maximum SNR: the input return loss of the LNA will be sacrificed due to the mismatching of the input impedance to 50 ohm. A typical method used in designing an input matching network displays noise circles and gain/
loss circles of the input network on the same Smith chart ([4], pp. 295–308). The noise figure of an amplifier can be estimated by the following expression:
F F R
amp
n S opt
S opt
= + ⋅ ⋅ −
(
−)
⋅ +min
| |
| | | |
4
1 1
2 2
Γ Γ
Γ Γ 22 (3.29)
1.9 pF 4.4 pF S
75.5 nH 183 nH
f = 200 MHz
Figure 3.3
Maximum power matching circuit (conjugate).
Fmin, Γopt, and Rn (equivalent noise resistance of a transistor) are generally specified in the transistor data sheet. Therefore, by choosing different ΓS
values, we can control the value of the noise at the amplifier output. When ΓS = Γopt, the noise figure value Famp is minimal and equal to Fmin. If we lack such data for noise optimization, we may use a noise figure meter to find the optimal value experimentally.
3.3.7 Output gain Matching for Noise Matched lNA
After we obtain a specific LNA noise value, then based on the procedure described in Section 3.3.6 covering noise minimization, we can use an addi-tional procedure as the last step in designing an output matching circuit.
This design procedure provides a reasonable noise figure and acceptable amplifier gain. The noise minimization procedure transforms the existing source reflection coefficient ΓS to the new value Γ1S that allows us to calculate the resulting output reflection coefficient Γ1out
Γ Γ Because the maximum gain approach is based on a conjugate-matched out-put port, we must create an outout-put circuit to transform the system termina-tion to the required conjugate-matched source. The final step is to transform the system load termination to the complex conjugate of this new Γ1L = Γ*1out. This method is known as the available gain design outline [6]. Amplifiers designed on this principle achieve a perfectly matched output port with a mismatched input port.
The mismatch loss at the input determines the magnitude of the input reflection coefficient. For example, if we have to sacrifice a 1 dB gain at the input port for the best noise value, the 1 dB mismatch loss converts to a 0.45 input reflection coefficient magnitude. A 2 dB mismatch loss leads to an input reflection coefficient magnitude of 0.6—a poor input match.
3.3.8 low Noise Amplifier Distortion Parameters
Active RF devices are ultimately nonlinear in operation. When driven with a large RF signal, a device will generate undesirable spurious signals. A 1 dB gain compression point parameter is a measure of the linearity of a device and is defined as the input power that causes a 1 dB drop in linear gain due to device saturation. A 1 dB gain output compression point is related to the 1 dB gain input compression point as follows (dBm scale):
P1dB(output)=P1dB(input) (+ GAIN− 1) (3.31) When two or more harmonic signals are applied to a nonlinear amplifier, the output contains additional frequency components called intermodulation
products. For example, if two sinusoidal signals of frequencies f1 and f2 are applied to an amplifier, the output signal contains frequency components n f⋅ ± ⋅1 m f2 (n and m are any integers). The frequencies 2f1 and 2f2 are the second harmonics, f1 ± f2 are the second-order intermodulation products, and 2f1 ± f2 and 2f2± f1 are the third-order intermodulation products. The special problem with third-order products is that they can fall within the operating frequency band. We know ([4], p. 363) that the ratio of a 1 dB out-put power compression point and a third-order product outout-put power level can be estimated (dBm scale) as follows:
P outputIP3( )≈P1dB(output)+ dB 10 (3.32) Also, it can be shown that:
P2f1=3Pf1−2PIP3 (3.33) where P2f1 and Pf1 are power levels of harmonics with frequencies of 2f1 and f1, respectively.
The spurious free dynamic range DRANGE of an amplifier is defined as:
DRANGE=2 PIP m + m− AMPBW F−
3[ 3(dB ) 174dB 10log ( )dB −−X( )dB −Gamp( )].dB where AMPBW is the amplifier frequency bandwidth defined as the differ-ence between the frequency limits of the amplifier that corresponds to 3 dB signal attenuation. A typical value of X(dB) is 3 dB.
3.3.9 Measurement Set-up to estimate Third-Order intermodulation Distortions
Two continuous wave (CW) signal generators with equal power levels are set a few megahertz apart, near the low end of the specified frequency band. The test is repeated in mid-band and near the high end. The fundamental tone lev-els are set so as not to saturate the amplifier tested. The test equipment has not contributed too much of its own IM (intermodulation). The power combiner and attenuators ahead of the amplifier promote isolation between RF genera-tors that could produce IM internally. Low-pass filters reduce harmonics that could add to distortions generated by the amplifier. The output third-order intercept point (Figure 3.4) is computed from the measurements as:
P output P P A A
IP3
1 2
( )= + − MAX2( , ) (3.34)
where A1 and A2 are the power levels of harmonics 2 . f1 – f2 and 2 . f2 – f1 and P is the amplified power of the CW signal generator. A1, A2, and P are read on a spectrum analyzer in dBm. The input third-order intercept point is PIP3 (input) = PIP3 (output) – G (dB scale); G is the gain of the amplifier tested.