aspects of wide-band, linear
HF power amplifiers
When designing wide-band, linear HF power amplifiers a small number of basic rules should be considered. These are not very complicated but should be followed rather carefully when the object is to maximize power and efficiency. With these basic rules firmly into position, further details will follow quite naturally.
These basic design rules apply to LF and HF amplifiers although each of these fields also exhibit additional requirements that are specific to the particular range of frequencies. With basic design rules comparable, still many radio-amateurs have no problems designing LF amplifiers and will shy away from their home-brow linear HF power equivalents. The short notes in this article will discuss these basic design rules for radio-hams to start thinking about designing their own amplifiers from available components, probably already present in the junk box.
In tuned, single frequency amplifiers the choice of the system impedance is less important as most internal parasitic impedances will be part of a designed-in impedance that will be tuned to the desired operating frequency.
In wide-band systems, system impedance Z0 is one of the primary selections. This impedance in principle is a freely selectable quantity but somewhat restrained in practice.
As a general rule, the higher Z0, the lower system currents and therefore the lower the loss in all parasitic series inductances, resistances and further 'additional', series impedances. This premium is lost however in all parasitic (parallel) capacitances that will be unavoidable and will limit maximum frequency.
At a low system impedance, system currents will be high(er) and therefore all series-loss will increase. Because of the low impedance, parallel capacitance will be less important allowing for higher maximum frequencies.
From the above it follows system impedance selection to be connected to the desired frequency and frequency range of the amplifier, with the lower impedance range related to the higher operational frequencies. Figure 1 is presenting a general idea about the position of the system impedance, that does not have to be represented by an actual component and in practice usually isn't either.
System impedance also is an entity of choice and therefore be closely related to practical considerations e.g. availability and price of components designed for a particular characteristic impedance. To this extend one should think of transmission-lines, filters, sub-systems etc., but also that high-impedance inductors may be constructed from lower diameter, un-silvered wire and low-voltage capacitors usually also mean lower price. Although a system impedance of 50 Ohm for wide-band systems is a well known 'standard', 75 Ohm is a very good option and other impedances may be even better depending on local requirements.
At wide-band power amplifiers based on vacuum tubes it may be profitable to select a higher system impedance. A vacuum tube usually operates under a high-voltage, low(er) current 'regime' making matching impedances also of a higher level. Further more, (dipole) antennas only exhibit a rather low termination impedance (around 50 Ohm) when resonating and a much higher impedance outside resonance. Selecting a high 'system impedance' when matching an antenna to a tube amplifier therefore usually will require a lower transformer ratio which in general is more profitable from an efficiency point of view and also simpler to construct.
At wide-band power amplifiers based on semi-conductors a low impedance system impedance may be more profitable since transistors usually operate in a low-voltage high current regime. To match to a high(er) impedance antenna, an in-between step to an 'intermediate' system impedance usually is a practical solution to avoid high-step-up ratio's.
At power amplifiers a wide range of voltage-current regimes (impedance-level) may be encountered, amongst others depending of the type of active component. From a system point of view it is efficient to arrive at system-impedance level as soon as this is practical and to this extend a matching transformer usually is the component of choice. Parasitic effects are always a point of concern in wide band amplifiers. Therefore impedance matching ratio's should not be too high to avoid parasitic effects of the low impedance regime to influence the circuit at the high-impedance site and vise versa. In this respect one could think of (serial, leak) inductance as a factor of concern in the low-impedance regime and parallel and inter-winding capacitive effects at the higher impedance site. In practice and for high(er frequency wide-band amplifiers in particular, impedance ratio's of 1 : 16 already are very high, while 1 : 25 for LF amplifiers are run of the mill and very low when using vacuum tubes.
What parallel impedance?
A matching transformer is to match the lower impedance regime to the higher environment, preferably without being a 'matching factor' in itself. The transformer therefore should be more or less 'invisible' at system level, meaning to introduce as little loss and/or phase shift as possible. A practical rule of thumb to accomplish this is the transformer to exhibit four times the system impedance at the lowest operational frequency:
Zt = 4 x Z0,
At this parallel impedance, standing-wave
ratio will deteriorate to SWR 1,28 but will improve
at higher frequencies to become even more 'invisible'. The number of turns to
arrive at this impedance depends on the type of transformer core material,
for which the manufacturer will supply winding factor
Note! Most manufacturers define
TN36/23/15-4C65 toroide (
toroide (1.57" (
Recalculating the latter to the basic
definition will yield:
How many turns?
To calculate the number of turns for a
specific application, we may rework the equation: Zt
= w .
n = 0,8 √ ( Z0
/ ( f .
n = number of turns (at system impedance level)
Z0 = system impedance
f = lower operating frequency (Hertz)
Selecting 50 Ohm as the system impedance and
n = 13,7 √(1/f) (f in MHz. = lower operating frequency)
which would lead to 10 turns for a lower operating frequency of 2 MHz.
Note. More turns is not necessarily the better. At more turns than the required number the parasitic parallel capacitance will increase lowering the maximum operating frequency.
Depending on the actual operating frequency, the transformer core will be more or less lossy. Depending on the voltage across the transformer, some power will be dissipated in this core-loss and will heat-up the core. Several mechanisms will limit the maximum core temperature.
* Curie temperature. This number is related
to the maximum ferrite temperature, above which the material will lose all
permeability. This implies impedance to drop to very low values which usually
will destroy the component and / or the system it was embedded in. When the
system is going first, temperature will drop and material will return to the
usual permeability. This Curie temperature is very much related to the
specific ferrite material, e.g.
* Mechanical degradation. This is related to
the maximum core temperature of non-sintered materials e.g. electrolytic-iron
(hydrogen reduced) iron powder and Carbonyl iron powder. According to some
manufacturers, these materials will be permanently degraded when exposed to
* Winding materials temperature. Some
transformers will be constructed using transmission-lines, as in transmission-line
transformers. These lines are usually constructed from a soft, easily
deformable material that will loose mechanical integrity above
In general maximum temperature rise from internal heating for transformers and baluns is restricted to 30 K to also allow for high environmental temperature conditions as found inside power amplifier cabinets and at the antenna at a hot summer day.
A transformer at a
In the example transformer above, that required 10 turns for reasons of system impedance, maximum allowable voltage is: 10 x 42 Volt = 420 Volt at 2 MHz., leading to over 3,5 kW of system power in a 50 Ohm system or maximum 10 x 24 Volt = 240 Volt at 30 MHz., leading to around1,15 kW. When constructed from RG58 coaxial transmission-line, it will be this latter that limits maximum system power to 350 W. at 30 MHz. for reasons of maximum current handling capacity.
We prefer to discuss maximum voltage across the transformer over specifying maximum allowable system power. A well designed transformer may still be destroyed at much lower system power when system impedance is higher than designed for, as in a dipole antenna outside resonance. Within power limits, maximum voltage across the transformer may become easily too high leading to much higher internal core dissipation and finally destruction of this component and even the system driving this.
In table 1 an impression may be obtained of
the maximum allowable voltage across a one-turn inductor at the well known
Z = n2 x Zt.
Maximum voltage for more turns may be obtained by multiplying the voltage of this one turn inductor by the number of turns as in:
V = n x Vm.diss.
Maximum allowable system power may be obtained by taking the maximum, more turns voltage squared and dividing by the system impedance as in:
Ptrafo max. = (n x Vm.diss)2 / Z0.
The second column is the ferri-magnetic resonance frequency (fr) of the specific ferrite material. This is a materials parameter and is related to the reactance (μ') and loss (μ") parameters as the frequency where: μ' = μ" (Q = 1). It is inversely related to permeability, so 3E25 type of material representing the highest permeability and is therefore a low frequency material.
From table1 it may be seen two ferrite parameters to compete when determining maximum voltage across the inductor, i.e. permeability and loss, that both are frequency dependent, but in different ways. When finally loss will be the determining factor at a frequency above fr, maximum allowable voltages tend to arrive in the same ball-park.
Also, total impedance will still continue to rise long after this ferri-magnetic resonance frequency, which is very useful when designing choke type of applications.
The number of turns at the 'non-system side' of the transformer, and so the transformer ratio 'T', is still un-determined, but will follow from the system to match to. We will attend to this in the next paragraph. Independent of T, most important transformer parameter already have been determined like the core material, number of 'system-side' turns and maximum allowable voltage (system power).
The transformer will match one impedance to an other, but will not influence the power ratio from input to output, apart from a small amount of power loss. This is a 'no-brainer' but will often be forgotten when designing transformers. We will use this simple 'input power is equal to output power' rule quite often.
Background to various ferrite calculations may be found in the series of articles on this subject as in: Ferrites in HF applications' on this web-site.
What transformer type?
We discussed various transformer aspects, that may take different shapes depending on materials and shapes available. Also we discussed 'turns' and transformer ratio's in terms of the classic flux transformer, i.e. transformers where input is coupled to the output by means of the electro-magnetic field in the core. This transformer type will serve its purpose if well designed but is also suffering from inherent limitations, related to the mechanism of flux coupling and parasitic capacitance across and between 'windings'.
When core loss is becoming noticeable as a system parameter, i.e. around and after ferri-magnetic resonance of the core material, inter winding coupling is going down. This will be noticeable in the increasing of leakage flux, translating into a series inductance with the transformer which will limit high(er) frequency response. Together with the intrinsic transformer loss, this type of transformers will find their application limit around the ferri-magnetic resonance frequency, i.e. when μ' = μ" or Q = 1. More on this subject may be found at HF transformers.
A different type of transformers is consisting of one or more transmission-lines, that are combined in series or in parallel at the input and / or at the output. Transformer ratio is determined by directly adding currents and / or voltages and different transformer ratios may be created although somewhat less flexible than with flux transformers. Because of the inherent wide-band characteristics of these transmission-lines, this type of transformer may be applied over a much wider range of frequencies than the flux type.
Critical point at transmission-line transformers is the input to output separation. For this application, again core materials will be used to create a high input to output impedance. It is virtually unimportant how this high impedance is created, by loss, by reactance or a combination, which is leading to a much wider frequency application range of the same core material, as also may be appreciated from table 1.
As far as 'parallel impedance' at the transformer input is concerned, the same formula's apply as with the flux transformers. Because of a different circuit lay-out, a different strategy has to be followed for feeding DC-power to the active components.
More on transmission-line transformers may be found in: Transmission-line transformers.
As discussed before, power amplifiers may be designed with vacuum-tubes or solid-state devices or even a combination of the two. At the higher power range vacuum-tubes will usually be the preferred component as it is less difficult to remove the internally dissipated power that results from a less than 100 % system efficiency. Modern higher power broadcast stations may currently be equipped with solid-state output stages, although these have been design as a combination of a number (tens) of lower power solid-state amplifiers 'building bricks', combined to deliver the required high power output. This will also ensure higher system reliability when only one of these building bricks is failing. Whatever the active component, the design procedures are very much comparable.
As an example, we will start designing a power amplifier based on a real life transistor, BUZ308, although this type will not likely be applied in a final HF wide band-width power amplifier. The design procedure however will not be different.
The transistor manufacturer will supply a great number of parameters and specifications. To start-off we will look at some limiting values we should obey to exploit the life expectance for the component. For BUZ308 we find:
- maximum drain - source voltage: 800 Volt (Vmax),
- maximum drain current: 2,6 Ampere (Imax)
- maximum dissipation internally: 75 Watt (Pmax).
Other important information may be supplied
on the internal thermal conditions. According to specifications, maximum
silicon temperature is Tj =
Next we will look at transistor characteristics as in figure 2.
To our surprise we find numbers (far) above the maximum figures for this component (current) or not far enough (voltage). Usually this is meaning the component is (also) being designed for a number of pulse-type applications or specific high-voltage low-current circuits as in inductive switching. Further more this manufacturer has been so kind to also supply the maximum internal power rating as in the dotted line.
In figure 2 we find a number of horizontal lines for various gate voltages. When we follow the line for Vg = 4,5 V from high to low drain voltage, we find the curve to deviate from the horizontal line at around 15 V., curving back to 0V thereafter. This 15 V. point is called 'knee voltage' and is marking an area we should stay out for linear applications.
Whatever choices we like to make at designing this transistor power amplifier, we should take care to keep some margin to allow for adverse operating conditions e.g. switching to full power at less than ideal matching conditions (SWR > 1). Therefore we prefer to stay away by at least a factor of 1,5 from the earlier mentioned absolute limiting values. Our limiting values for the amplifiers we are designing therefore will be:
Id max. = Imax / 1,5 = 1,7 Ampere, Vd max. = Vmax / 1,5 = 530 Volt, Pmax = 75 / 1,5 = 50 Watt.
Class A amplifier
Different types of amplifiers may be designed around the selected transistor. We may remember class A amplifiers to operate at low distortion, so this might be our first try. In a class A amplifier, the active element is adjusted at the control port (at the BUZ308, the gate) so half the maximum current is flowing in the output terminal.
When selecting the maximum (calculation) drain current: Ip van 1,7 Ampere, at the knee voltage: 20 Volt, we may draw a straight line to the point where drain voltage is 80 Volt at drain current is 0 Ampere. This line is always below the dotted line for maximum allowed power so may be regarded as an allowed and safe load line. In figure 2 this is the red line.
With this load line, the power amplifier is completely determined. This may be appreciated since:
- At Id = 0 Ampere, no voltage may be found across an impedance in the drain circuit, so this voltage may be regarded as the supply voltage:
Vb = 80 Volt.
- Maximum output voltage as delivered to the load is equal to the supply voltage minus the knee voltage:
Vp = Vb - Vkn = 80 - 20 Volt = 60 Volt.
This is also the top-top value of the output voltage to the load, with an effective (rms) value of:
Vout = 60 / 2√2 V. = 21,2 Volt rms.
- Maximum current through the transistor (and the load) is 1,7 Ampere and minimum current is 0 Ampere. This is the top-top value of the output current, with an effective (rms) value of:
Iout = 1,7 / 2√2 A. = 0,6 Ampere rms.
- Out of the rms values for voltage and current we may calculate maximum power as delivered to the load:
Pout = Vout x Iout = 21,2 x 0,6 = 12,7 Watt
- Class A amplifier at no drive is set in the middle of the load-line, so at a drain current of:
IDC = Ip / 2 = 1,7 / 2 = 0,85 Ampere
which leads at the load line to a drain voltage of 50 V.
- Total delivered DC input power to the transistor is:
PT = VDC x IDC = 50 x 0,85 = 42,5 Watt.
- The efficiency (ή) of the power amplifier may be calculated in a percentage of the DC input
ή = (Pout / PT ) x100 % = (12,7 / 42,5) x 100 % = 29,9 %
This is considerably less that what we expect from a class A amplifier (50%) and is mainly due to the relatively high knee-voltage as compared to the supply voltage. The area below the knee is un-usable (outside linear voltage - current behavior) but is contributing to the total DC input power.
- The load-line may be directly translated into a load resistance, which may be calculated from AC peak voltage and current:
Rb = Vp / Ip = 60 / 1,7 Ohm = 35,5 Ohm,
This in turn is determining the output transformer, that will have an impedance transformer ratio of
35,5 : 50 = 1,4 : 1 , of which the turns ratio is following from the square route: 1,2 : 1.
With 10 turns at the primary side as calculated before, the secondary number is 10 / 1,2 = 8 turns.
Thermal requirements of the class A amplifier
The thermal requirements of a power amplifier are an important part of the design.
From the manufacturers specifications we
learn maximum internal temperature: Tj =
Difference between the amplifier input and output power (see also efficiency) is turned into heat, we may calculate:
PW = PT - Pout = 42,5 - 12,7 Watt = 29,8 Watt
Because of this power, a temperature gradient will exist across the thermal resistance of:
ΔT = PW x Rth j-mb = 29,8 x 1,67 = 49,8 K
Since maximum internal temperature is
Tmb max = 150 -
When we would like to operate this amplifier
at a maximum ambient temperature of: Tamb =
Rth heatsink = (Tmb max - Tamb) / PW = (100,2 - 35) / 29,8 = 2,12 K/W, and this is more than a simple cooling flap.
Some conclusion on class A amplifier
By selecting a class A
amplifier, we obtained a solution with a relatively low output power and a
low power efficiency. Furthermore the power supply will have to supply a
relatively high average current of
It is clear the class A choice to not be an optimal one, so we better investigate a different set-point (amplifier class).
In a class B amplifier, the active element is adjusted at the control port (at the BUZ308, the gate) so (just) no current will flow in the output terminal. When increasing the drive, drain current will flow in the positive half of the drive cycle and no current during the negative half. Since our amplifier is to be operated in the linear mode, we need two active elements that will each operate at the other half of the input drive. Both halves will be combined in the output transformer to generate the full output cycle. This also means each active element to deliver full power at half the time, or on average, half power during the full period. In the off half cycle, the active element will not dissipate any (DC or AC) power.
We may again operate each active element according to the red load-line of figure 2, since this has been selected for maximum drive and power as related to the absolute maximum ratings.
Note the transistor this time should be rated for double the drain voltage since the output voltage of the active device is added to the drain voltage of the non-active device, that is at supply voltage level at no drive.
At the selection of the load line, the complete amplifier is determined.
- At Id = 0 Ampere, supply voltage: Vb = 80 Volt.
- Maximum output voltage swing:
Vp = Vb - Vkn = 60 Volt.
This is the peak value of one drive period, the other half is generated by the second transistor. Effective voltage of this half cycle is:
Vout = 60 / √2 Volt = 42,4 Vrms.
- Maximum current is again 1,7 Ampere peak value, with an effective value of
Iout = 1,7 / √2
- During the half period cycle each transistor is generating
Pout = Vout x Iout = 42,4 x 1,2 = 50,9 Watt, and no power during the next half period when the other transistor takes over. Total output power for this class B amplifier therefore is also 50,9 Watt.
- Through each transistor a current is flowing only during the active cycle. Average value of this current is:
IDC = 2 x Imax / p = 1,08 Ampere.
DC voltage at the transistor is equal to the supply voltage, so total DC input power per transistor, per half cycle is:
P = IDC x VDC = 1,08 x 80 = 86,4 Watt, which is also total DC input power for the full drive cycle of this class B amplifier.
- Total efficiency of this class B amplifier again is calculated as a percentage of total DC power as delivered to the amplifier:
ή = (Pout / PT) x 100 % = (50,9 / 86,4) x 100 = 58,9 %.
This again is lower than the theoretical maximum for this class of amplifiers (68%) again because of the relatively high knee voltage.
- Drain load (load-line) per transistor is
the same as in the class A amplifier, making also
turns ratio (per transistor) identical. The output transformer therefore will
have a turns ratio of (1+1) : 1,2 or (8 + 8) :
Thermal requirements of the class B amplifier
Calculations are running in parallel to those in the class A amplifier. Power as delivered to the amplifier that is not delivered to the output, will be generated in heat and should be drained away to below permissible temperatures. For this class B amplifier and per transistor:
PW = PT - Pout = 43,2 - 25,5 Watt = 17,8 Watt.
This will generate a temperature gradient in the transistor from junction to mounting base:
ΔT = PW x Rth j-mb = 17,8 x 1,67 = 29,6 K
The maximum allowable mounting base temperature therefore will be
Tmb max = 150 -
When we would like to operate this amplifier
at a maximum ambient temperature of: Tamb =
Rth heatsink = (Tmb max - Tamb) / PW = (120,4 - 35) / 17,8 K/W = 4,8 K/W.
When we prefer one mounting base for the two transistors, thermal resistance will be halved to 2,4 K/W.
Comparing class A to class B amplifier.
To compare the class A to the class B amplifier, table 2 has been generated:
In table 2 it is immediately clear what the efficiency difference between the two amplifier classes is bringing. At about double the input power by the power supply, the class B amplifier is delivering four times the output power and will require about the same heatsink as the class A amplifier.
Since each transistor in this class B amplifier is taking DC current per cycle, no net DC current will flow though the output transformer so full drive capabilities are available for HF-power with inherent lower distortion.
This example is showing it pays to go for amplifiers with high efficiency because of the positive effects at various system components. Selecting a low 'knee-voltage' transistor will further improve efficiency.
Note, all calculations have been performed at full output power. At lower (average) HF output power as in SSB operation, average efficiency will also be lower.
In a practical class B amplifier each transistor usually will not be adjusted to a no-current at no-drive situation. Starting from zero drive, the first part of the transistor characteristic is not very linear, generating harmonic content in the output current. By adjusting each transistor to a small 'resting current' this non-linear drive area may be avoided. This amplifier-setting is called a class AB amplifier since the set-point is somewhere in-between class A and class B. At this set-point however, transistors are operating in class B mode for most of the time.
The class AB setting is requiring some additional DC power that will not be delivered to the output and so will make total efficiency of this class somewhat lower then full class B amplifier, with additional (small) requirements to the heatsink.
A second practical point concerns the transistor un-equality. Even from the same manufacturing batch, transistors will always exhibit small differences as to their characteristics. This may result in one transistor to still be completely switched-off with the other transistor already fully at the class AB drain current for the same set-point. A second effect may be noticeable at the output with one transistor delivering full power and the other just keeping a 'toe in the water'. These undesired situations we of course very much like to avoid.
An effective way of dealing with these effects is to apply some form of feed-back, for instance by having a small portion of total drain current to deliver a voltage across a source resistor. This voltage will effectively be in series with the input drive and set-point, but in the opposite phase. This feed-back voltage will have a positive and equalizing effect to transistor drive characteristics to the DC (set-point) as well as to AC (linearity). As a rule of thumb, source voltage should be in the range of 10 - 30 % of the gate voltage at full drive swing, this to be applied even when transistors are selected for pairing.
With these feed-back resistors, linearity will be improved and so output harmonic content will be lowered. Since this a an HF amplifier, these source resistances should be of a 'no-inductance' type and also of sufficient power handling capacity since source currents may be high.
To enhance current drive capabilities, more transistors may be connected in parallel. To ensure good tracking of characteristics, the same principles of feed-back apply.
As for the calculations (load-line, power delivery and handling, heat considerations), the same principles apply. Because current are doubling (for two transistors in parallel) the same characteristics of figure 2 apply, this time with doubled current figures on the vertical axes. With three transistors in parallel the figures obviously triple, etc.
Note, the matching transformer also to match to a lower impedance, with half the primary impedance for two transistors in parallel one third at three transistors etc. All further calculations will follow the, by now familiar patterns as above.
- With the above method it should be not too difficult to design a power amplifier with components already available from the junk-box (transistors, ferrite cores, heatsink etc.).
- Although high linearity is always a design requirement for wide-band amplifiers, this should be balanced to other practical requirements as system efficiency and available drive and DC input power.
- High system efficiency usually translates into simpler requirements to the heatsink, power supply and will result in more output power.
- The higher the amplifier class (A, AB, B, C, currently also D and E are practical), the higher system efficiency although not all classes may be applied in wide-band linear amplifiers.
The next project phase is concerned with practical system construction. To this phase, practical experience is an important requirement and usually means battling with al sorts of parasitic and non-ideal effects, that are becoming more important as frequency rises. Therefore it is important for a starting designer to study the designs of experienced people, with the principles as explained in this article as a basis. In this way the practical learning curve will be less steep and my help starting your own amplifier design
Bob J. van Donselaar.