rf elec notes v1_1 section 11-12 annotated

11 Power amplifiers Power amplifiers (PA) are required for applications that need to deliver RF power to a load, e.g. the final output stage of a transmitter might need to deliver anything from a few milli-watts to many kilo-watts into an antenna. For some types of modulation such as AM, SSB, QAM or CDMA, where the amplitude of the modulated carrier is not constant, the whole transmission path including the power amplifier is required to be linear. Hence power amplifier operation is confined to classes A or AB. For other types of modulation however, such as FM, FSK or PSK where the amplitude of the modulated carrier is constant, power amplifiers can use non linear modes such as class C. An important consideration in RF power amplifiers is efficiency. In battery-powered portable transmitting equipment, the PA typically consumes most of the power so achieving the highest efficiency is important. Efficiency of an amplifier is defined as: Average RF Output power into the load Average DC power consumption from supply Two basic steps in PA design are to bias the active device(s) to operate in the required mode (Class A, B, C, etc.) and to design input and output circuits that provide a conjugate match and hence optimise power transfer into and out of the device. The conjugate matching networks described in a previous section can be used but in the case of RF power devices, the input and output impedances are typically much less than 50 Ω, possibly of the order of 1 Ω or less.

11.1 ' Class 'A In a Class 'A' amplifier, the DC bias exceeds the total signal swing. The active device in a Class 'A' amplifier is never driven into saturation or cut off (provided it is operating in its linear region, i.e. not over-driven). The conduction angle is 360° of an RF cycle. Virtually all small signal RF (and audio) amplifiers operate in Class 'A'. A Class 'A' amplifier is linear and is therefore suitable for all types of RF signals whether amplitude modulated or not, i.e. AM, SSB or FM signals. A significant disadvantage of Class 'A' is poor efficiency so that for an RF power amplifier, the active device needs to have a higher power dissipation capability and more substantial heat sink compared to Class 'B' or 'C'. A Class 'A' PA consumes more power than a Class 'B' or 'C' amplifier with the same RF output power, which is an important consideration for battery powered equipment, The maximum possible efficiency for a Class 'A' amplifier is 50%. This is with an inductor or transformer as the collector or drain load for a BJT or FET, which would be true for almost any practical RF power amplifier. This maximum efficiency is only possible when the amplifier is driving the maximum possible amplitude into the load, i.e. just before 'clipping' occurs. This means that for an RF power amplifier that is handling an amplitude modulated signal, (e.g. AM or SSB), the average efficiency is much less than 50%. In the case of a small-signal low frequency BJT amplifier (e.g. audio) with a resistive collector load, it can be shown that the maximum efficiency is 6.25%.

Version 1.0, D.M.Lauder Page 77 ©2009 University Of Hertfordshire

11.2 Class 'B' A Class B amplifier normally uses a pair of active devices in a 'push-pull' configuration. In 'pure' class 'B', there is no standing DC bias and the conduction angle is exactly 180° of an RF cycle for each device, i.e. one device handles the positive half-cycles and the other device handles the negative half-cycles. The efficiency is up to 78%. The amplifier is linear and is therefore suitable for AM, SSB or FM signals. In the case of Class 'B' RF power amplifiers (and early transistor audio amplifiers), a driver transformer and an output transformer are normally used, as shown in the Class AB amplifier below.

11.3 Class AB In practice, a 'pure' Class 'B' amplifier suffers from 'crossover distortion' at the zero-crossing points of the signal. To overcome this, a certain amount of standing DC bias is normally applied, which results in Class AB operation where the conduction angle for each device is more than 180° of an RF cycle but less than 360°. A Class AB 'push-pull' amplifier is shown below. It is similar to a Class 'B' 'push-pull' amplifier but T1 and T2 have forward bias provided by R4. Driver transformer TR1 matches the input source impedance into the input impedance of T1 and T2and it also acts as a phase-splitter so that one half-cycle of the RF waveforms is handled by T1 and the other half by T2. Output transformer TR3 matches the output impedance of T1 and T2 to the load impedance and also acts as a combiner, combining the two half-cycle outputs from T1 and T2. Class AB amplifiers may use a single active device or a pair of active devices in push-pull. Any Class AB amplifier has sufficient forward bias applied to the transistor(s) to ensure conduction for between 180-360 degrees of an RF cycle. This enables linear operation and improves efficiency compared to class A. The push-pull class AB amplifier shown below uses broad band transformer matching techniques.

OUTPUT to filter INPUT

T1

T2TR1 R2

R3

TR2

C5

C6

R4

C1

C7

TR3

RFC

C2+Vcc


11.4 Class C A Class 'C' amplifier can be used at RF but not for audio, It uses a single active device with zero DC bias, as shown in the circuit below where the base of T1 is DC grounded via RFC1. The conduction angle is less than 180° of an RF cycle. Amplifiers of this type are highly efficient, typically 60 - 80% for 120 - 150° conduction angle but can only operate over a relatively narrow bandwidth. This is because the collector load (L2, C2) needs to be resonant. A Class 'C' amplifier is inherently non-linear and is therefore suitable for constant amplitude signals such as FM only. In the circuit below, C1 and L1 match the source impedance (e.g. 50 Ω) into the input impedance of T1. RFC1 grounds the base of T1 at DC while providing an RF impedance that is high compared to the input impedance of T1. RFC2 provides a path for DC supply current to the collector of T2 while providing an RF impedance that is high compared to the output impedance of T2. L2 and C2 form a resonant circuit and also match the output impedance of T1 (typically a few ohms or less) to the required load impedance (e.g. 50 Ω). C4 is a DC blocking capacitor because the DC voltage on L2 is +Vcc.

T1

RFC2

L1

C1

C2

RFC1

L2

C3

C4

+Vcc

OUTPUT

INPUT

Note that if some forward bias is applied to T1 in the above circuit, by connecting RFC1 to a DC bias source instead of to ground, the class of operation changes from Class C to Class A or Class AB (depending on the amount of bias current).

11.5 Power Amplifier Modules A simple solution to PA design is to use a modular PA. These devices are available from many manufacturers and provide a power gain block in a single module. Input and output matching networks are included in the module to match to a specified impedance (usually 50 Ω). A PA module can normally operate over a limited range of frequencies, for example a mobile phone band. All that is needed is a power supply, some supply decoupling and filtering. A wide range of power outputs are available and corresponding input drive levels are required. This type of solution is compact and reliable but can be costly. The outputs of multiple modules can be combined in cases where high power output is required.


11.6 Linearity in RF amplifiers There are certain cases where an RF circuit element is non-linear. • Mixers must be non-linear in order to operate. • Class 'C' RF power amplifiers are inherently non-linear but are only suitable for

transmitting signals whose amplitude is constant, e.g. FM or PSK. Although the non-linearity generates harmonics, these can be reduced by low-pass or band-pass filtering at the output.

In most other cases however, an RF amplifier is required to be linear but in practice, linearity is not perfect. This can lead to the generation of unwanted harmonics and/or intermodulation products. In a transmitter, such unwanted products result in spurious outputs, where some power is radiated on frequencies other than the intended frequency. This can result in interference to other users of the radio spectrum. In a receiver, such unwanted products result in spurious responses, where the receiver has an unwanted response to signals on frequencies other than the wanted frequency. It is therefore necessary to be able to analyse non-linearities in linear RF amplifiers and to ensure that linearity is good enough for the required application. An ideal linear amplifier gives an output that is directly proportional to the input:

Vo(t) = K.Vi(t) Where Vo(t) = output voltage, Vi(t) = input voltage K is ideally a constant (but in practice, it may vary with frequency)

Vo(dB)

Vi(dB)0

Amplitude Characteristics a Linear Amplifier


For a single sinusoidal input, a spectrum analyser would show:

f

V

f

KVVi(f) Vo(f)

11.6.1 General Representation of Non-Linearities Non-linearities in amplifiers or RF systems can lead to second (and higher) order terms in Vi(t) appearing at the output:

Vo t K vi t X vi t Y vi t higher( ) . ( ) . ( ) . ( ) . . . . . .= + + +2 3 order terms

Where: K=system voltage gain (Av), X & Y are the distortion coefficients Some terms may be absent or may be at an insignificantly low level. Consider the effects of the 2nd order term on the performance of the system shown below when a sinusoidal input is fed into it:

Av=K

Vsin t Vo(t)ω

For this system we then have:

Vo t K vi t X vi t( ) . ( ) . ( )= + 2

2 2

where vi(t) = Vsin t

hence Vo(t) = K.Vsin t + X.V sin t

ω

ω ω

But Sin2 a = 0.5(1 - Cos 2a), hence........

Vo t K V t X V t

or K V t X V t

( ) . sin . ( cos )

. sin . cos

= + −

+ −

ω ω

ω ω

12

1 2

12

2

2

2 Vo(t) = X.V2

2

Where:

OUTPUT WANTED theist KVsinHARMONIC SECOND theist cos2

TERM DC a is 2

2

ωω

XV

here, the input is a pure sinusoid but the system caused the distortion.


A spectrum analyser would show these distortion components as follows:

f

V

f

KVVi(f) Vo(f)

0

0.5XV2

2f

11.6.2 Intermodulation Distortion (IMD) Intermodulation distortion (IMD) is caused by the interaction of two or more signals in a non-linear device or system giving rise to unwanted output signals called intermodulation products (IMPs). Consider a linear device such as an amplifier where two sine waves with equal amplitude are fed into the system simultaneously so the input is of the form:

Vi t V t V t( ) sin sin= +ω ω1 2

If the device is perfectly linear, the only frequencies present at the output will be the input frequencies f1 and f2. If the device is non-linear however and it causes 2nd order terms to be generated the output will contain the following components.

f1

V

f1

KVVi(f) Vo(f)

0

0.5XV2

2f1f2 f2 2f2f2-f1 f1+f2

XV 2

Depending upon the characteristics of the non-linearity, it may generate second order, third order or higher order intermodulation products. In the case where f1 and f2 are nearly equal, third order intermodulation products such as 2f1 ± f2 and 2f2 ± f1 are particularly undesirable because they fall close to f1 and f2 so they cannot easily be removed by bandpass filtering. What undesirable effects to IMPs have in transmitters? What undesirable effects to IMPs have in receivers?


12 Passive Filters A passive filter is a network of passive components designed to exhibit a specific frequency response. Many possible topologies exist where the generic form of the transfer function is;

ncj

ViVo

⎥⎦

⎤⎢⎣

⎡+

=

ωω

1

1

fc = filter cut-off frequency, n = the order or number of poles in the response

12.1.1 Bode Plots If we plot the filter output voltage against frequency we can see exactly how the filter will respond to a range of input frequencies. The axes can be either linear to obtain the linear frequency response or logarithmic to obtain a bode plot. The Bode Plot is a straight line approximation that requires a log-log plot, i.e. logarithmic frequency axis and logarithmic amplitude axis. Normally, the amplitude axis has a linear scale in Decibels, which are proportional to the log. of amplitude.

12.1.2 Roll-Off Roll-off is a measure of how well the filter will reject frequencies outside the passband and is defined as the slope of the bode plot of the response at fc. Roll-off is often quoted in dB per octave where an octave represents a factor of two along the frequency axis. Alternatively, it can be quoted in dB per decade where a decade represents a factor of 10 along the frequency axis. Either way, the more poles (n) in the filter response, the steeper the slope and the better the out of band rejection. Roll- off is approximately 20n dB/decade or 6n dB/octave.

12.1.3 Passive High Pass Filters (HPF) A first order passive HPF has the characteristics shown below. The example shown has a cut-off frequency of 1 MHz.


HPF roll-off is a measure of how well the filter will reject frequencies below the cut-off frequency (fc). Roll-off in this case is defined as the slope of the bode plot below fc. We will look at two ways of implementing this characteristic.

12.1.3.1 Single Pole RC HPF

If we configure a resistor and capacitor as shown below, the reduction in capacitive reactance (Z1= Xc) as we increase the input frequency means that less voltage is dropped across the capacitor and so by KVL the output voltage must increase. Eventually, Xc = 0 and so Vo = Vi thereafter - we have a simple HPF.

C

R

Vi

lg f

20lgVo(f)

Vo Vi

CRTan CR

CR=

+= =−

1 11 1

221

ωθ ω

πτ f = CRVo c

12.1.4 Passive Low Pass Filters (LPF) A first order passive LPF has the characteristics shown below. The example shown has a cut-off frequency of 1 MHz.

LPF roll-off is a measure of how well the filter will reject frequencies above the cut-off frequency (fc). Roll-off is defined as the slope of the bode plot above fc.

Version 1.0, D.M.Lauder 4 ©2009 University Of Hertfordshire

12.1.4.1 Single Pole RC LPF As the input frequency is increased above fc, the reactance of the capacitor is progressively reduced, thus Vo is steadily reduced. As the frequency is decreased below fc, the reactance of the capacitor progressively increases, thus less and less voltage is dropped across the resistor and so Vo tends towards Vi.

C

R

Vi

lg f

20lgVo(f)

Vo Vi

CRTan CR

CR=

+= − =−

1

122

1

ωθ ω

πτ f = CRVo c

12.1.5 Passive Band Pass Filters (BPF) A BPF is a circuit where the attenuation is low within a defined range of input frequencies (the PASS BAND) whilst outside the PASS BAND the attenuation is large. This type of response is used widely to ensure that a system responds only to a wanted band of frequencies but not to other higher or lower frequencies, for example tuned RF amplifiers in radio transmitters and receivers. A bandpass filter can be implemented in two different ways. First a high-pass filter and a low-pass filter can be cascaded. This is suitable for filters with a relatively wide passband. Alternatively, a passive bandpass filter can be implemented using L-C resonant circuits. Examples of both types are shown below for a generic BPF.

lg f

20lgVo(f)

f

Vo(f)

Cascaded LPF and HPF (Bode plot) Resonant BPF (linear amplitude and frequency scales)


12.1.5.1 Quality Factor (Qo) and Selectivity Selectivity is the ability of the filter to select in-band frequencies and reject those out of band. An indication of filter selectivity is obtained in the form of its Q-factor (Qo). Higher Q circuits are more selective.

12.1.5.2 Two Pole LCR Series Resonant BPF Resonant (tuned) circuits are widely used to obtain relatively narrow passbands for example in radio frequency applications where we may wish to tune to a specific transmission and reject adjacent channels.

C

R

ViL

Vo

f

Vo(f)

Vo Vi

L R CRTan L R CR=

+ −= − −−

1 11

21

( ) ( )( ) (

ω ωθ ω Vo )ω

f = LR

1R

BW = fQo

o

o= = =

12

1π

ωωLC

QCR

LCo

o

o

At some frequency we can note that XL = XC hence VL = VC, since VL and VC are of opposite signs the phasor sum will cancel, leaving all of the voltage across the resistor. This frequency is


known as the resonant frequency (fo) at which the circuit is purely resistive giving zero phase shift. At frequencies below fo, the capacitor has more influence since XC > XL, the circuit is predominantly capacitive and so we have positive phase shift. At frequencies above fo, the inductor has more influence since XL > XC, the circuit is predominantly inductive and so we have negative phase shift.

12.1.5.3 Two Pole LCR Parallel Resonant BPF (Tank Circuit)

Vi

C

R

L

Vo

f

Vo(f)

[ ][ ])()(

)()(11

Vo2LRCRTan

LRCR

ViVo ωωθ

ωω−−=

−+= −

Qo and fo are the same as for the series circuit

12.1.6 Multiple pole filters We noted generally, that the roll off of a filter can be increased if more poles are present in the response. An ideal 'brick wall' filter has a perfectly flat passband and infinitely steep roll-off but this requires an infinite number of poles and cannot be implemented in practice. Numerous texts cover detailed filter design and many CAD packages offer simple facilities with which to design higher order filters using Butterworth, Chebychev or Bessel polynomials. A Butterworth filter response has a maximally flat passband. A Chebychev filter response provides the highest possible rate of roll-off for a given order of filter but it is necessary to accept a specified amount of passband ripple (e.g. 0.1 dB, 1 dB) A Bessel filter has a linear phase response. Multi-pole bandpass filters are an important building block in radio receivers, for example for use in the IF or RF amplifier. Such filters are generally fixed frequency filters because it is not generally practicable to vary the centre frequency of such a filter.


12.1.6.1 Multiple Pole Passive HPF The example below shows a 7th order Butterworth high-pass filter with a cut-off frequency of 900 MHz, designed using the Filter Design tool in TINA.

Out

R6

50

C6 7.9p

L5 7

.1n

C4 2p

L3 4

.4n

C2 2p

L1 7

.1n

C0 7.9pR6 50

+U

06Highpass Filter


12.1.6.2 Multiple Pole Passive LPF The example below shows a 7th order Butterworth low-pass filter with a cut-off frequency of 900 MHz, designed using the Filter Design tool in TINA.

Out

R6

50

L6 3.9n

C5

4.4p

L4 16n

C3

7.1p

L2 16n

C1

4.4p

L0 3.9nR5 50

+U

05Low pass Filter


12.1.6.3 Multiple Pole Passive BPF The example below shows a bandpass filter designed using RFsim99. This has a 10.7 MHz centre frequency and a relatively narrow bandwidth. This type of filter could be used as an I.F. filter in a superhet radio receiver.

E.g. Butterworth BPF, fc = 10.7 MHz, BW = 25kHz

It should be noted that any filter needs to be designed to operate with a certain source and load impedance, which normally needs to be resistive. This may be 50 Ω in some cases but other impedances such as 330 Ω or 2 kΩ may be used in crystal and ceramic bandpass filters for I.F. amplifiers. For an IF Filter, 4, 6 or 8 poles may be required in order to achieve a sufficiently sharp roll-off outside the passband. It may not be practicable to implement such a filter design using inductors and capacitors because the values of L or C or the required 'Q' factors may not be practical. For example in the above filter design, the values of the capacitors are all less than 1 pF and the stray capacitance of the inductors would need to be extremely low. Instead, such filter designs may require crystal or ceramic resonator elements. Such resonators use piezo-electric materials such as quartz or Barium Titanate. For frequencies up to about 70 MHz, the mode of operation is a bulk acoustic wave. For higher frequencies such as 100 - 2000 MHz, the mode of operation is a Surface Acoustic Wave (SAW). SAW filters are used for IF and RF bandpass filters in mobile communications equipment and other applications.

21s Arg s21


rf elec notes v1_1 section 11-12 annotated

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