5.2 VHF Broadband Class-E PA
5.2.1 Matching Network Design
Load/source-pull simulation is implemented to get the optimum load and source impedances for the targeted band. This simulation is implemented for each single frequency between 225 MHz and 400 MHz with 50 MHz step. The load harmonic impedances were terminated with high impedances, i.e.,>1000Ω. The harmonic source impedances were ignored during the simulation as they have a minor effect on the efficiency.
Fig. 5.10 represents the load pull simulation for three frequencies in the target band. This figure shows the PAE, output power and DC-current contours with 2 %, 0.5 dB and 600 mA steps, respectively. It is shown in this figure that the optimum impedance contours decrease with frequency for the PAE and output power. A very interesting result is the current contours which are never closed its contours. The black dots shown in Fig. 5.10 are the optimum load impedances used in the design. Those impedances are chosen so that they are near to each other and can give smooth behaviour over the frequency.
Fig. 5.11 shows the optimum load and source impedances for PA in the targeted band. As it can be seen from this figure, the optimum load impedance has a constant phase, i.e.,≈52◦, and its magnitude reduces with the frequency with a constant slope, which follows (5.12):
ZLopt =
{ RLopt(1+j1.28) , @f = f0
∞ , @f =n f0, n is an integer > 1 (5.12) whereRLopt is the optimum real load impedance. The best function that fits the figure shown in Fig. 5.11 is a linear function in (5.13):
RLopt =−0.0378f+41.1538 (5.13) The variable f in (5.13) represents the frequency in MHz, in the targeted band.
Those equations are implemented ideally in ADS as a linear impedance function. The result from the load/source-pull performance is shown in Fig. 5.12, where the PAE exceeds 87 % and the output power is 47 dBm (50 W) with 14 dB Gain.
Designing the broadband Class-E SMPAs requires a matching network integrated with the filter that terminates the harmonic with an open impedance. Making a filter that has this termination is a straight forward procedure, see [23]. However, the source and load impedances for the filter are 50Ω. Hence, a matching network that must match the optimum load impedances
70 5. VHF and UHF Broadband PA
Pout Id0
PAE
Zopt
(a)
Pout Id0
PAE
Zopt
(b)
Pout
Id0 PAE
Zopt
(c)
Figure 5.10:Load-pull contours for the output power (red) with step 0.5 dB, drain efficiency (green) with 2 % step and DC current (blue) with 0.6 mA step for a) 225 MHz, b) 312 MHz and c) 400 MHz. the black dot is the realised load impedance.
of the transistor to a 50Ωis required prior to the filter. This matching network should not produce a short circuit for the harmonics, i.e., without shunt capacitor or shunt series LC network. Fig.
5.13 shows the proposed concept of the circuit topology. From the figure, a bandpass filter is chosen because it can give better termination, i.e., high impedance, compared to a low pass filter.
The first element in this bandpass filter should be a series LC network connected in series to give high impedance termination for the harmonics. The matching network can be designed using a one section ladder network and adding a series inductor as shown in Fig. 5.14.a. This network avoids the shunt capacitor that can give low impedance for the high frequency (i.e.;
harmonics). The matching network is a high pass network, which passes the high frequency starting from the fundamental. Also, its first element (i.e.; the inductor) gives high impedance for the high frequency and its second element (i.e.; the capacitor) gives low impedance for the high frequency. Fig. 5.14.b shows the synthesis of the matching network after each element in the matching network. A parallel inductorLM1moves the output impedance along the admittance circle toward the upper half of the Smith chart. The series capacitanceCM1moves the resulted
5.2 VHF Broadband Class-E PA 71
|ZS|[Ω],∠ZS[◦]
-80 -60 -40 -20 0 20
Freq. [MHz]
200 250 300 350 400 450
|ZS|
∠ZS
(a)
|ZL|[Ω],∠ZL[◦]
30 40 50 60
Freq. [MHz]
200 250 300 350 400 450
|ZL|
∠ZL
(b)
Figure 5.11:Ideal optimum a) source impedances and b) load impedances over the entire band according to the load/source-pull simulation.
impedance along the impedance circle toward the lower half of the Smith chart. The last elements in this matching network moves along the impedance circle to the upper half of the Smith chart, the brown line in Fig. 5.14.b. With an appropriate filter, the load impedance can be matched over the frequency completely as with using the bandpass filter. Table 5.1 shows the lumped element values used in Fig. 5.14.
The filter type is an important issue in this design. As stated previously, a broad-band Class-E PA requires a constant phase and magnitude of a constant slope (5.12). Hence, a Butterworth filter was chosen. It is well known that a Butterworth filter has a flat gain and relatively constant phase compared to other filter types. However, a Class-E PA requires high rejection at the harmonics.
In the targeted band, the first harmonic (i.e.; 450 MHz=2×225 MHz) is very close to the band edge frequency (i.e.; 400 MHz). A roll-off of 80 dB/decade (i.e.; 4-poles) is implemented. This should give a better rejection at the second harmonic.
Furthermore, to minimize the insertion loss of the filter, it is designed with 3 dB bandwidth for the band between 212 MHz and 441 MHz. The circuit topology for the bandpass filter could be a T or aπnetwork, where T networks behave as an open impedance for the stop-band (i.e.;
Pout[dBm],Gain[dB]
10 20 30 40 50
Efficiency[%]
80 85 90 95 100
Freq. [MHz]
200 250 300 350 400 450
PAE η Pout Gain
Figure 5.12: Ideal performance for the transistor with ideal load/source-pull impedances; output power (red), gain (blue), drain efficiency (green) and power added efficiency (black).
72 5. VHF and UHF Broadband PA
Pin Q
Id OMN BPF
IDC Vdd
RL + Vo
− Io(t)
Figure 5.13: Proposed circuit diagram topology consists of output matching network (OMN) and band-pass filter (BPF).
harmonics) andπnetworks behave like a short for the stop-band. Therefore, the T network was chosen to fulfil the design requirements of Class-E PA. The filter can be designed normally using any CAD tool or by following filter design books as in [23] (5.14)-(5.17).
Lsn= 50gn
BWfω0 (5.14)
Pin Q
Id
CM1
LM1
LM2
BPF IDC
Vdd
50Ω + Vo
− Io(t)
ZL Z1 Z2 Z3 Zf inal
(a)
f
1f
1f
1f
1Z
LZ
1Z
2Z
3Z
f inal(b)
Figure 5.14:Load matching network synthesize showing a) circuit impedance network and b) Load impedances for each element in the matching network.
Table 5.1:Ideal lumped element values for the output matching network used to design broadband VHF PA.
Lumped element LM1 CM1 LM2
Value 33 nH 3.9 pF 36 nH
5.2 VHF Broadband Class-E PA 73 Csn= 1
Lsnω20
(5.15) Cpn= gn
50BWfω0 (5.16)
Lpn= 1
Cpnω20 (5.17)
whereLsnand Lpn represent the series and the parallel inductor in the filter, respectively. The BWf and ω0 are the fractional bandwidth and the geometric centre frequency, they are equal to(ω2−ω1)/ω0 and√
ω1ω2, respectively. gn are the element values of the filter for 1Ωand 1 rad/sec, andnis the number of filter element (i.e.; poles).
Fig. 5.15 shows the filter circuit diagram. It is clearly seen from (5.14)-(5.17) that the lumped elements in the filter are designed with respect to the geometric centre frequency which is equal to 305.8 MHz for the designed filter. As a result, the optimum output impedances can be translated into a 50−jXCF1(f0)at the geometric centre frequency, Fig. 5.16. The first capacitor element in the filter, i.e.,CF1, is equal to 10 pF which results into 52Ω. The result of Fig. 5.16 is shown in Fig. 5.14.b with Z3 symbol. The final result of the output matching network is shown in Fig. 5.14.b, represented with theZf symbol.
5.2.1.1 DC-Feed Design
To this point, the output matching network was designed using ideal lumped elements, and the input source impedance is implemented using a function that describes it over the bandwidth.
The input and output DC-feed was implemented using ideal high inductance with an ideal shunt capacitor. The main goal of the DC-feed is to isolate the RF component from the DC source, which can damage the source. However, DC sources produce low frequencies that might cause a severe oscillation for the PA. Hence, a broadband DC feed that blocks the RF components, i.e., fundamental and harmonics, must give a short circuit for all other frequencies. To make this, multiple series inductors, having a resonance occurring on the fundamental band, are implemented.
Parallel capacitors with different values are introduced after each inductor, as shown in Fig. 5.17.
In this figure, the doted line is shown here to represent the repetition of the seriesLparallelCi. In most cases, these lumped elements have the same values. In Fig. 5.17, transmission lines are used at the start and at the end of the inductors. Those transmission lines used as pads for the
− + Port 1
CF1 LF1
CF2 LF2 CF3 LF3
CF4 LF4 CF5 LF5
50Ω + Vo
− Io(t)
Figure 5.15:Butterworth bandpass filter used in the matching network of the designed PA.
74 5. VHF and UHF Broadband PA
Pin Q
Id
CM1
LM1
LM2
Z@f0 =50−jXCF1 IDC
Vdd
Figure 5.16:Matching network design to include the first series capacitor of the band-pass filter.
transistor, in addition, can be optimized to shift the resonance frequency to the targeted band.
The first element in the output matching network, shown in Fig. 5.16, is a shunt inductor. This shunt inductor can be used as part of the DC-feed, i.e., for high frequency. Hence, the ground path of this inductorLM1can be presented with a group of shunt capacitors, as in the DC-feed, to block the DC current from the ground and to give a low impedance for the targeted frequency.
After those parallel capacitors, the DC feed circuit shown in Fig. 5.17, starts from the first pad of the inductor.
5.2.1.2 Input Matching Network
The total performance is optimized in the targeted band. The input matching network is designed in two steps. The first step is the stability circuit with the DC-feed network. The final step is to
− + Port 1
+
− Port 2 L
C1 C2 C3
Figure 5.17:Drain and gate DC-feed network used in the PA design including the bypass capacitors, the dots here represent a multi section of the same DC-feed network.
5.2 VHF Broadband Class-E PA 75 match the source equation to 50Ω, the generator resistance.
5.2.1.3 Stability Circuit
As discussed before, oscillation suppression techniques are implemented on the input side to decrease the gain at low frequencies. A series resistance with DC-feed (R1) and another series resistance (R2) in series with transistor gate is implemented to reduce the low frequency and high frequency oscillation, respectively. Another two parallelRC networks are implemented at the gate side. Usually, the capacitance in this kind of circuit is implemented here in order to pass the desired signal over the targeted band. This can be implemented using capacitors that have series resonance on the pass band. In other frequencies, the parallel resistance will be seen by the signal and, hence, will be attenuated. Finally, a seriesRCnetwork is implemented parallel to the signal path which suppresses the extreme low frequency oscillation. Fig. 5.18 represents the stability matching network used in this design. The values of the stability elements are chosen so that the transistor is unconditionally stable, and the maximum gain is maximized over the targeted band.
This insures stability of the PA regardless of the external networks and maximum possible gain from the transistor, see Fig. 5.19.
The input matching network is implemented using a three segment ladder network usingL andCelements. These elements give a flexible control on the input matching network to fit the desired source impedance shown in Fig. 5.11.b.
5.2.1.4 Realization
An equivalent matching network consisting of a real lumped element, transmission lines and a short stub is implemented for the final realization. Air Core inductors from coilcraft and SMD multi layer capacitor from ATC ceramics were used in the final realization. These lumped
−
Vin
+ IMN
R5
C3
C2
R4
C1
R3
R2
R1 Igg
Vgg
Q1 Id
IDC
Vdd
+ Vd
−
OMN
RL
+ Vo
− Io(t)
Figure 5.18:The designed PA circuit with the stability circuits.
76 5. VHF and UHF Broadband PA
K
0 1 2 3 4 5
Freq. [GHz]
0 2 4 6 8 10
Kno stab. ckt Kwith stab. ckt
(a)
Gmax[dB]
-20 0 20 40 60 80
Freq. [GHz]
0 2 4 6 8 10
Gmax no stab. ckt Gmax with stab. ckt
(b)
Figure 5.19: Simulation without stability network (solid) and with stability network (dashed) for a) K-factor and b) maximum gain.
elements must be chosen so they meet the following criteria:
High quality factor: It is also in relation to low series DC resistance. This ensures lower losses in the operating band.
High resonance frequency: Making the lumped elements to work as they should behave for high frequencies. This is important to terminate the harmonic as the ideal design.
High power handling capabilities: For an inductor, it is the maximum RMS current value. For a capacitor, it is usually the maximum voltage difference between the parallel plate.
Transmission lines are introduced here in order to fine-tune the impedances for the input and output matching network. Usually, the values of the inductors with high quality factors are not given in the market with high selection flexibility as by the capacitor. Hence, one more pole is added to the designed filter in the output matching network. One more shunt inductor, between seriesCM1and seriesLM2, is also added in the output matching network to give a better flexibility of fine-tuning the matching network. A further step of optimization was necessary in the final design to meet the required specifications. Rogers substrate withεr=3.38 and a thickness of 0.51 mm is used as an implemented PCB for this PA. Fig. 5.20 shows the manufactured PA.