QPSK Modulator

In cellular phones and other digital, portable, wireless communication devices, three parameters are becoming increasingly important. Low power consumption and lightweight batteries give the device the power of freedom of movement, higher front-end receiver sensitivity increases the receiving distance, and higher front-end linearity has a direct impact on the allowable dynamic range. With the use of non-constant energy modulation schemes such as π/4DQPSK and 8QAM, the importance of the above three parameters is increasing.

SiGe (Silicon Germanium) technology is a recent technological innovation that can improve receiver power consumption, sensitivity and dynamic range at the same time. GST-3 is a new high-speed IC process based on SiGe technology, which features a characteristic frequency (f _T ) of 35 GHz. The typical front-end block diagram below (Figure 1) shows the performance that can be achieved (1.9 GHz) with a mixer and low noise amplifier (LNA) implemented in SiGe technology.

Figure 1. A typical wireless receiver circuit, including a low-noise amplifier and a mixer.

Noise Performance of SiGe Devices

The main influence on noise figure in the downlink is the noise generated by the first transistor input stage of the LNA. Noise figure (NF) is a parameter that reflects the performance of the network and is used to compare the noise in the actual network with the noise in the signal after passing through an ideal noise-free network. The noise factor (F) of an amplifier or other network with power gain G = P _OUT /P _IN can be expressed as:

NF is a measure of the degradation of the signal-to-noise ratio (SNR) from the network input to the output, usually expressed in dB: NF = 10log ₁₀ F, therefore:

F = Input SNR/Output SNR
= (P _IN /N _IN )/(P _OUT /N _OUT )
= N _OUT /(N _IN ^. G)

We are only concerned with thermal noise (also called Johnson noise or white noise) and shot noise (also called Schottky noise). A specific high-frequency equivalent model of a bipolar transistor (Giacoleto model, see Figure 2) will help us understand how this noise is generated. This model also tells us how SiGe technology reduces the noise figure of the LNA front end.

Figure 2. A detailed npn transistor model (Giacoleto model) simplifies the analysis of frequency effects. Thermal and shot noise of silicon germanium materials

In a conductor with a temperature greater than zero (0°K), random motion of charge carriers generates random noise voltages and currents. As the temperature of the conductor increases, the random motion of these charge carriers increases, which increases the noise voltage. The thermal noise generated by the parasitic base resistance (Rbb′) of the transistor is Vn(f) = 4kTRbb′, where Vn(f) is the voltage noise spectral density in V ² /Hz, k is the Boltzmann constant (1.38 . 10 ^-23 Joules/Kelvin), and T is the absolute temperature in Kelvin (°C + 273°).

Shot noise is a result of the particle nature of charge carriers. The DC current flowing in a semiconductor is usually considered to be constant at every moment, but any current is formed by the movement of individual electrons and holes. Only the time average of the current generated by these charge carriers can be considered a constant current. Any fluctuation in the number of charge carriers will produce a random current at that moment, which is shot noise.

The noise spectral density of the shot noise in the base current is Inb(f) = 2qIb = 2qIc/β, where Inb is the noise spectral density of the current in I ² /Hz, Ib is the DC bias current of the base, q is the charge of an electron (1.6 . 10-19 coulombs), and β is the DC current amplification factor of the transistor. Therefore, the total noise spectral density generated by the transistor input stage is the sum of thermal noise and shot noise:

γn = 4kTRbb′ + R _SOURCE 2qIc/β

Maxim's new silicon germanium process, GST-3, is developed from GST-2 (a bipolar process with a characteristic frequency of 27GHz) by doping the transistor base with germanium. The result is a significant reduction in the Rbb' value and a significant improvement in the transistor's beta value. Accompanying these two changes is a better noise figure for silicon germanium transistors (compared to silicon transistors with the same collector current). The noise figure of a transistor is usually expressed as:

F = 1 + [ Vn ² (f) / R _SOURCE + Inb ² (f) x R _SOURCE ] / 4kT

For both silicon bipolar transistors and silicon germanium transistors, the noise figure in the above equation is minimum when R _SOURCE = Vn(f)/Inb(f). Therefore, an LNA with a source impedance close to this value can maximize the advantages of silicon germanium technology.

Another important issue in wireless design is the degradation of noise figure over frequency. The power gain of a typical transistor roughly fits the upper curve in Figure 3. Considering the transistor equivalent circuit in Figure 2, this curve is not surprising. In fact, the equivalent model is an RC low-pass filter with a gain drop of 6dB per octave. The frequency at which the current gain (β) of the theoretical common-emitter circuit is 1 (0dB) is called the characteristic frequency (f _T ). The gain of the LNA depends directly on β, so the degradation of the noise figure [F = N _OUT /(N _IN G)] starts from the point where the gain gradually decreases.

Figure 3. Silicon germanium (SiGe) bipolar transistors exhibit high gain and low noise.

To see how the GST-3 silicon germanium process improves the noise figure at high frequencies, consider doping the p-type silicon base of a transistor with germanium. This lowers the bandgap across the base by 80mV to 100mV, creating a strong electric field between the emitter and collector junctions. This field causes electrons to move quickly from the base to the collector, shortening the transit time (t _b ) required for carriers to cross the narrow base region. All other things being equal, reducing t _b increases f _T by about 30%.

For transistors of the same area, SiGe devices require only 1/3 to 1/2 the current required by GST-2 devices to achieve a given f _T. Higher f T reduces high-frequency noise because β begins to taper off at higher frequencies.

Ultra-Low-Noise Silicon-Ge (SiGe) Amplifier (MAX2641)

The MAX2641, based on silicon germanium technology, has incomparable advantages over silicon bipolar LNAs, whose NF begins to deteriorate near 2GHz (e.g., 1.5dB at 1GHz, 2.5dB at 2GHz). The high reverse isolation of silicon germanium devices means that tuning the input matching network has no effect on the output matching network, and vice versa.

The silicon germanium device MAX2641 is best suited for operation in the frequency range of 1400MHz to 2500MHz, where typical performance is 14.4dB gain at 1900MHz, -4dBm input IP3 (IIP3), 30dB reverse isolation, and 1.3dB noise figure (see Figure 4). The MAX2641 is packaged in a 6-pin SOT23 package, uses a single power supply of +2.7V to +5.5V, draws 3.5mA of current, and is internally biased. The only external components typically required are a two-element input matching circuit, input and output isolation capacitors, and a V _CC bypass capacitor.

Figure 4. Note the very low noise figure of this SiGe integrated low-noise amplifier.

Linearity of SiGe Devices

In addition to noise and bandwidth, communication systems are also limited by signal distortion. The effectiveness of a system depends on its dynamic range (the range of signals that the system can process with high quality). Dynamic range is affected by the noise figure, which has a lower limit defined as sensitivity and an upper limit defined as the maximum amount of acceptable signal distortion. Achieving the best dynamic range requires a trade-off between power consumption, output signal distortion, and input signal value relative to noise.

The typical receiver block diagram (Figure 1) shows the importance of noise figure and linearity of the LNA and mixer. Because the input of the LNA is a very weak signal directly from the antenna, NF is a critical parameter. For the mixer, its input is the amplified signal output by the LNA, so linearity is its most important parameter.

The output signal is never an exact replica of the input signal because no transistor is perfectly linear. The output signal always contains harmonics, intermodulation distortion (IMD), and other parasitic components. In Figure 5, the second term in the P _OUT equation is called second harmonic or second-order distortion, and the third term is called third harmonic or third-order distortion. They are characterized by the presence of a pure sinusoidal signal at one or two frequencies that are close in frequency at the input of the next stage. For example, the third-order intermodulation distortion of the MAX2681 is a -25dBm signal consisting of two frequencies at 1950MHz and 1951MHz.

Figure 5. Testing of two frequency signals characterizes harmonic distortion and intermodulation distortion.

_{A graph of the P OUT} equation in the frequency domain shows that the output contains the fundamental frequencies ω1 and ω2, the second harmonic frequencies 2ω1 _and 2ω2 _, the third harmonic frequencies 3ω1 _and 3ω2 _, the second-order intermodulation product IM2, and the third-order intermodulation product IM3. Figure 5 also shows that in cellular handsets and other systems with narrowband operating frequencies (e.g., frequencies of tens of megahertz and frequency spans less than one octave), only the IM3 spurious signals (2ω1 _- ω2 ₎ and (2ω2 _- ω1 ₎ fall within the filter passband. The result is distortion of the desired signals at frequencies _ω1 and _ω2 .

In the lowest terms of the output power in the P _OUT formula, coefficient K1A is directly linearly proportional to the input signal amplitude, K2A ² is proportional to the square of the input amplitude, and K3A ³ is proportional to the cube of the input amplitude. Thus, the curve drawn using logarithmic coordinates is a straight line with a slope in the order of the response.

Second-order and third-order intercept points are commonly used parameters to indicate performance. The higher the intercept point, the better the device is able to amplify large signals. At high power values, the output response will be compressed and deviate from the expected response value. This deviation point (Figure 6a) is defined as the 1dB compression point, which is where the actual output signal is compressed by 1dB compared to the output value inferred from the linear portion of the curve (G _1dB = G - 1dB).

From the MAX2681 data sheet, P _OUT has a -56dBc spurious-free dynamic range (SFDR) relative to IM3 (Figure 6b) at frequencies above 1900MHz. Typical operating conditions are PRF _{IN = -25dBm, IIP3 = 0.5dBm, and conversion gain = 8.4dB. LO-to-IF leakage and other spurious products can be filtered out by a narrowband IF filter, as shown in Figure 1. The MAX2681 (silicon germanium double-balanced downconverter) typically only draws 8.7mA of I CC} current when the performance requirements are met .

Figure 6. A SiGe double-balanced downconverter provides low (0.5dBm) IIP3 values ​​and 56dBc dynamic range (b).

Another silicon germanium downconverter (MAX2680) has different performance characteristics. It is packaged in a tiny 6-pin SOT23 package and consists of a double-balanced Gilbert cell mixer with single-ended RF, LO, and IF ports. Like the MAX2681, it operates from a single supply of +2.7V to +5.5V, accepts an RF input between 400MHz and 2500MHz, and produces an IF output frequency between 10MHz and 500MHz. Supply current is typically less than 0.1µA in shutdown mode. The LO input is a single-ended broadband port with a VSWR better than 2.0:1 (400MHz to 2.5GHz).

Input sensitivity of SiGe front end

To estimate the front-end sensitivity using the MAX2641/MAX2681 SiGe downconverter, consider a QPSK modulated signal with a 4MHz signal bandwidth. To simplify the calculations, assume that the input filter has an ideal rectangular filter characteristic. First, consider the 3dB insertion loss introduced by the antenna converter and the front-end passive filter. It is necessary to add 3dB to the NF (AntNF). Next, add a filter after the LNA to remove the distortion generated by the LNA (other than IM3). For this purpose, consider a filter with 2dB attenuation and NF. At 1900MHz, add the LNA post-filter NF to the MAX2681 11.1dB NF:

Total NF = filter NF + mixer NF =
2dB + 11.1dB = 13.1dB

The input of the LNA needs a good NF value because it gets a very weak signal directly from the antenna. The mixer NF is reduced by the gain of the LNA:

Total NF = LNA NF + (1/G _LNA )(NF _TOTAL - 1) = 2.054;
NF _TOTAL (dB) = 10log2.126 = 3.12dB.

Using QPSK modulation, the minimum required signal energy to noise energy ratio at the antenna input is Eb/No = 6.5dB when BER = 10 ^{-3 . The noise floor of the absolute noise at +25°C is AbsNfl = -174dBm = 10log(KT), where T = +300°K, K = 1.38 . 10 -23} . The filter bandwidth in dB is FiltBwth = 10log(4MHz) = 66dB. For a QPSK modulated signal with a BER of 10 ^-3 , the front-end sensitivity in Figure 1 is estimated by the following formula:

Input sensitivity = AbsNfl + AntNF + FiltBwth + NF _total + Eb/No
= -174dBm + 3dB + 66dB + 3.12dB + 6.5dB = -95.38dBm.

in conclusion

Silicon germanium (SiGe) technology can provide lower noise figures at frequencies above 1.0GHz compared to pure bipolar processes. It also reduces supply current and has higher linearity. Maxim has achieved high-linearity SiGe mixers with 0.5dBm IIP3 at 1900MHz, 11.1dB noise figure (SSB), 8.4dB conversion gain, and only 8.7mA supply current. The higher characteristic frequency (f _T ) of SiGe devices allows the devices to operate at higher frequencies, enabling applications at frequencies above 5GHz.

References

1. Richard Lodge, "Advantages of SiGe for GSM RF Front-Ends." Maxim Integrated Products, Theale, United Kingdom.
2. Chris Bowick, RF Circuit Designs. (Howard W. Sams, & Co. Inc).
3. Tri T. Ha, Solid-State Microwave Amplifier Design. A Wiley-Interscience publication, 1981, ISBN 0-471-08971-0.