16 2. Power Amplifier Characteristics
Pout[dBm],Gain[dB]
0 10 20 30 40
η,PAE[%]
0 20 40 60 80
Pin[dBm]
0 5 10 15 20 25
Gain Pout
PAE η Pout,1dB
Pin,1dB
Figure 2.3:Typical performance for a power amplifier versus input power.
2.2 Linearity and Distortion 17
2.2.1 Single Tone
Single-tone measurements are the basic method of the RF power amplifier to quantify linearity performance. If the input signal for a PA is expressed as:
vi=γcos(ωt) (2.11)
whereγis the amplitude of the input signal andωis the radial operating frequency. The output power can be obtained from (2.10) as:
vo= α2γ2
2 + (α1γ+3
4α3γ3)cos(ωt) +α2γ2
2 cos(2ωt) +α3γ3
4 cos(3ωt) (2.12) As it can be observed from (2.12), the output voltage contains harmonic components in addition to the fundamental and DC components. The voltage gain for the fundamental component is expressed as:
vo
vi = (α1+3
4α3γ3) (2.13)
It is evident from (2.13) that the gain is proportional to the cubic input voltage amplitude (γ). This gain compresses if and only if theα3is negative; otherwise it will expand, which is not a nature of the nonlinear devices. This gain shows the compression discussed before, which is usually referred to as the maximum input that can be applied to a RFPA without distorting the signal, in Fig. 2.5. For the other harmonic component in (2.12), it can be easily seen that the output harmonic power (P= v2
2R) increases twice as fast as in the fundamental power for the second harmonic and three times as fast as in the fundamental power for the third harmonic, Fig. 2.6.
2.2.1.1 AM-AM/AM-PM
AM-AM is a measure of the compression between the output and the input waveforms and can simply be expressed by the gain expression. AM-PM is a measure of the change in the output
VoltageGain[dB]
0 5 10 15
vi[dB]
0 5 10 15
Gv,1dB
Vi,1dB
Figure 2.5: Voltage gain compression as in (2.13).
18 2. Power Amplifier Characteristics
Pout[dBm]
-10 0 10 20 30 40
Pin[dBm]
0 5 10 15 20 25
Pout,sec
2
3 Pout,third Pout,f und
1
Figure 2.6: Single tone output power for the fundamental, second harmonic and third harmonic.
phase that depends on the input amplitude, expressed as:
AM−PM=ϕo(vi) (2.14)
whereϕoandviare the output phase and the input amplitude components, respectively. Usually, these parameters are plotted versus the input power, Fig. 2.7.
2.2.1.2 Total harmonic distortion
The harmonic distortion due to n-order of harmonic is defined by:
HDn= Pout,n
Pout,f und (2.15)
An ideal operation for a PA requires zero harmonic distortion (HDn). Higher value of this parameter reduces the efficiency of the power amplifier and increases the nonlinearity.
AM-AM[dBm],AM-PM[deg.]
-10 0 10 20 30
Pin[dBm]
0 5 10 15 20 25
AM-PM
AM-AM
Figure 2.7:Typical AM-AM/AM-PM curves for power amplifiers.
2.2 Linearity and Distortion 19 In a straightforward manner, the total harmonic distortion is defined by:
T HD=
∑
n≥2
Pout,nth
Pout,f und (2.16)
The above expressions are usually expressed on a logarithmic scale with reference to the funda-mental (dBc). This describes how far the harmonic powers are from the fundafunda-mental power.
2.2.2 Multi Tone
Single tone measurements and analysis give limited information regarding the linearity perform-ance. In reality, the input signal for a PA is not a single tone signal. Hence, a multi tone test gives a better picture of the distortion that might appear on the output signal of a PA. In this section, analysis for a two-tone signal is presented and discussed. Nevertheless, the same analysis applies for higher-order tones.
2.2.2.1 Intermodulation distortion
In reality, the input signal of a PA consists of two closely spaced frequencies f1and f2(f1< f2).
For simplicity, in this analysis both signals will be assumed to have an equal amplitude:
vi=γcos(ω1t) +γcos(ω2t) (2.17) Applying (2.17) in (2.10) and making some mathematical simplifications, the output signal is given by:
vo= α2γ2
+ [α1γ+9
4α3γ3][cos(ω1t) +cos(ω2t)]
+ α2γ2
2 [cos(2ω1t) +cos(2ω2t)]
+ α3γ3
4 [cos(3ω1t) +cos(3ω2t)] (2.18)
+ α2γ2[cos(ω1t+ω2t) +cos(ω1t−ω2t)]
+ 3α3γ3
4 [cos(ω1t+2ω2t) +cos(ω1t−2ω2t) +cos(2ω1t+ω2t) +cos(2ω1t−ω2t)]
The output voltage from the two-tone input signal contains an infinite number of a combination
20 2. Power Amplifier Characteristics from these tones in the form of:
n f1±m f2 (2.19)
wherenandmare integers≥0. The sum of these products gives the order of distortion. The second-order intermodulation products of two signals at f1and f2would occur at f1+f2, f1−f2, 2f1and 2f2, as shown in Fig. 2.8. From this figure, it can be concluded that the even products are out of band and, hence, they are less important than the odd product. Furthermore, the most influential odd product on the fundamental component is the third-order intermodulation product (IMD3). It is because of being the closest product to the fundamental component and highest amplitude component compared to the other odd products.
2.2.2.2 Intercept point
If the third intermodulation power is plotted with the fundamental tone versus the input power, new parameters can be extracted from this plot called the third order intercept point, as shown in Fig. 2.9. This point can be referred as the third order input intercept point IIP3 and third order output intercept point OIP3. They are usually known to be 10 dB higher than the 1-dB compression power for the one tone power [21]. From Fig. 2.9, it can be seen that the IMD3has a 3-dB slope versus the input power on the logarithmic scale. Usually, for the measurement, this is valid for the low power drive. However, when the power increases, the fifth order becomes more effective, and the translated IMD3from this order become more visible. Hence, for higher input power, the IMD component will have higher slope than 3-dB relative to the input power.
If the phases of the third- and fifth-degree coefficients are equal, the total IMD3responses will expand. However, if the phases are opposite, the IMD3distortion will be locally reduced. This explains why notches (sweet-spots) in the IMD3(and high-order) have been reported at certain amplitudes of output power.
PSD
f2−f1
2f2−2f1
3f2−3f1
f
f2+f1 2f2 2f1
4f2−3f1 3f2−2f1 2f2−f1 f2
f1
4f1−3f2 3f1−2f2
2f1−f2
IMD3
Figure 2.8:Output frequency component of an amplifier excited by a two tone signal.
2.2 Linearity and Distortion 21
Pout[dBm]
-60 -40 -20 0 20 40 60
Pin[dBm]
0 10 20 IIP3 30 40
OIP3
1Pout,f und PIMD3
3
Figure 2.9:Third order intercept point example.
2.2.3 Dynamic Signal
The previous two sections discussed the linearity with respect of discrete frequency input signals.
However, modern communication standards have many frequency components that need a more precise measure for the linearity. An important measure of the linearity for a dynamic input signal is the adjacent channel power ratio (ACPR) or adjacent leakage power ratio (ACLR). Fig.
2.10 shows the typical spectrum for a UMTS signal for a PA. From this figure the ACPR can be defined as the ratio of the power in the main band (carrier band) to the power in the adjacent band (adjacent channel), mathematically:
ACPRu=
∫
BcPout(f)d f
∫
BA1Pout(f)d f (2.20)
ACPRl=
∫
BcPout(f)d f
∫
BA2Pout(f)d f (2.21)
whereBc,BA1,BA2,ACPRuandACPRl are the signal bandwidth, the upper adjacent bandwidth, the lower adjacent bandwidth, the upper ACPR and the lower ACPR, respectively. Generally speaking, the power amplifier must meet certain ACPR depending on the applied input power.
For example, for a WCDMA signal, both bandwidths for the carrier and the adjacent channel are 5 MHz without any spacing between them. The ACPR must be more than -45 dBc [22].
Spectrum[dBm]
Freq. [Hz]
Carrier Signal
Adjacent Signal BC Adjacent Signal
BA2 BA1
Figure 2.10:Typical spectrum for a UMTS signal for PA.
22 2. Power Amplifier Characteristics ACLR has the same definition as the ACPR but the output power is filtered through the system filter and (2.20) and (2.21) can be applied directly.