### Ganella`s Transmission

```Mihai Albulet
윤석현


Broadband impedance matching 이 최선이라도, 종래
의 transformer 는 거의 RF power amplifier 에서 유용
하지 않다.
Basic Limitation of the convention Transformer.


Primary 와 secondary coil에 걸린 voltage 는 coil 의 감긴 수
(turn) 에 비례.
Coli 에 흐르는 전류는 감긴 수에 반 비례.
2
n 
R   1  RL  n 2 R L
 n2 
n
n 1
n2

The following presentation of these frequency limitation is
base on the lumped equivalent circuit of the wideband
transformer shown in figure 2-73


R'L  n 2 RL Is the load resistance referred to primary winding
r1 is the series resistance of the primary winding
r '  n 2 r 2 is the series resistance of the secondary winding

referred to the primary
Rc models the power loss in the magnetic core

Fig 2-73 을 low, middle, high 로 주파수 범위 구분하여
equivalent 회로 만든다.
Mid band 에서 리액턴스 값 무시.
Rc may be ignored, although it should be included in the
equivalent circuit if the power level is high and/or the power
loss in the magnetic core is significant

Lower frequency
The capacitance and the leakage inductance are negligible
Shunt inductance Lp become important
Shunt inductance Lp 가 low frequency 제한의 주 원인.



High frequency
The Capacitance and the leakage inductance become
important .
Lp and Rc negligible, and r’1 and r’2 are usually ignored


In the transmission-line transformer the coil are arranged so
that interwinding capacitance combine with the inductance to
form a transmission line.
As a result, the high-frequency response is limited by the
parasitics which have not been absorbed into the
characteristic impedance of the transmission line or by the
deviation of the characteristic impedance from its optimum
values

The bifilar coil is usually constructed by coiling a
transmission line around a ferrite core, or by threading the





Bifilar coil 에 흐르는 전류를 odd-mode (io) 와 even mode(ie) 로
나눌 수 있다.
the odd-mode current 는 무시할만한 external magnetic field
를 발생.
그 결과, adjacent turns 사이에서 magnetic coupling 이 발생하지
않고 , 같은 길이의 전송선과 같아 진다.
The even-mode current 는 in-phase equal magnetic fields 발
생, 그 결과 인덕턴스가 높을 때 standard coil L 과 같아 진다.
Inductance L이 상당히 높으면 , even-mode 전류는 무시 할 만큼
작아지고, odd-mode 로만 작용.
(a) The bifilar coil behave as a delay line.
(b) Fig 2-78 은 phase inverter. L 의 리액턴스가 RL 보다 커지면 단
지 odd-mode 로 전류 흐른다. V1 과 V2 는 out-of-phase.
(c) Fig 2-78은 balun (balanced-to-unbalanced) configuration
RL 의 중심이 left off 이면 두 windings 의 전류는 equal 이고
opposite 하다.
The reactance of RL is connected to ground, as shown in fig 278( c) ,the reactance of L must be far greater than RL to
assure that the even-mode currents are negligible and the

Fig 2-79
The two bifilar coils are in parallel at the low-impedance side
(signal source) and in series at the high-impedance side(the load)
Characteristic impedance Z0=RL/2 , R=RL/2 (Fig 2-80)


Characteristic impedance Z0=nRL , R  n2 RL (Fig 2-81)
Guanella’s transmission-line transformer 제한
1.
2.
3.
transmission-line 의 characteristic impedance 에 의해 흡수
되지 않은 parasitic 성분 .
주파수에 따른 Z0 의 변화.
증가하는 주파수에 따른 transmission-line 에서 power loss 증
가.
-
Low-frequency model of Guanella’s 1:4 Transmission-Line
Transformer -
1. the circuit is used as a balun with floating load, i.e ,
Only terminal (1,5) is ground. The low frequency response is
given by the magnetizing inductance (that shunt the signal
source), comprised of winding 3-4 in series with winding 6-5.
a.
b.
If two transmission lines are coiled on separate core, the
magnetic inductance is the sum of the two inductance (3-4
and 6-5).
If two transmission lines are coiled on the same core, the
magnetic coupling between them must be considered.
2. The circuit is used as an unun transformer, with terminal (1,5)
And 2 connected to ground. Consequently, winding 1-2 is
shorted, as is winding 3-4.
a. If two core are used, winding 5-6 and 7-8 are not affected by
shorted winding 1-2 and 3-4. 저주파 응답은 winding 5-6
and 7-8 에 의해 제공됨. 둘 사이에 magnetic coupling 발생.
b. If one core is used, winding 5-6 and 7-8 are also shorted,
resulting in a very poor low-frequency response.
If a good low-frequency unun transformer response is needed,
it is best
Ruthroff’s Transformer-line Transformer
Ruthroff’s Transformer-line Transformer mainly sums a direct
voltage (or current) with a delay voltage (or current ) , which
transverses a transmission lines.

a. Winding 은 충분한 길이의 리액턴스를 가진다. 그래서 단지 oddmode current 가 bifilar coil 에 흐른다.
b. 이 회로의 주요 목적은 signal source Vs 로부터 Load RL 까지
wide frequency band 내에서 power 의 maximum 전송을 얻는
것이다.


The low-frequency model of the Ruthoff 1:4 transformer is
shown in Fig 2-87
이 회로는 1:4 autotransformer 와 매우 유사함.

•
Fig 2-87 (a) 의 더 간단한 형태가 Fig 2-87 (b)
Core magnetizing inductance LM 의하여 shunt 된 ideal
transformer 로 대체됨.
Low frequency 를 향상시키기 위한 방법은 LM 증가.
 LM 의 증가 방법
a. Bifilar coil 의 turn 수 증가.
b. Magnetic coil 의 permeability 증가
c. Coil 의 effective cross-sectional area 증가
d. 코일에서 average magnetic path length 감소
a, c 는 전송선 길이의 증가에 의해 발생.
•

A general synthesis procedure for an arbitrary m : n
impedance ratio (where m and n are integers)
2
2
이 기술은 Guanella’s circuit 과 비교해 더 복잡하고 확장적 기술.

Fig 2-90 은 3:5 voltage ratio transformer ( 즉 9:25 impedance
ratio)

Fig 2-91 은 bottom transformer line 이 1:4 Ruthroff unun 로
연결. Top transformer line 은 Guanella 1:1 balun 로 연결.
problem
a. The overall gain must be relatively flat over the operating
frequency range fmin …. fmax.
b. The input VSWR of the amplifier must be kept within a
specified range (for example, 2:1 or lower) over the
operating frequency range.
두 가지 문제가 각각 따로 논의 되었더라도 각각의 문제는 서로 완전히
분리 할 수 없다.
두 가지 문제 모두 amplifier input 과 feedback path의 다양한
R,C,L 성분에 의해 해결 된다.

Broadband amplifier 에서 gain disparity 는 10~15 dB 보다 훨씬 크다.
Gain leveling 의 가능한 해결책은 frequency-dependent shunt
feedback 을 사용.
Cf is a DC-blocking
capacitor.
Lf tend to increase
The impedance of
the feedback path with
The operating frequency,
Preserving amplifier gain at
Higher frequencies
At lower frequencies, the feedback become stronger, decreasing
amplifiers gain as well as the input impedance Zin

Fig 2-96 은 degenerative feedback
CE reduce the gain at low frequencies
이미터 회로에서 원하지 않는 parasitic capacitance 를 제거 하기 어
려움.
Gain leveling can also be accomplished using RLC network, as
Fig 2-97.
At low frequencies, L has a low reactance while C has a high reactance.
그 결과 base-emitter junction 의 power 양 감소 ->Overall gain 감소.
At high frequencies, L 과 C 는 power gain을 보존하는 R1 , R2 영향을 제
거함. 그래서 input impedance는 주파수 또한 변화시킴.
Four-reactance networks can also be used for broadband
matching (see Fig 2-99).
A four-reactance networks is able to transform load impedance
R into Rin, at two frequencies.
Three basic procedures can be used to obtain a high-power AM
signal: 1. base bias modulation 2. AM signal amplification
3.collector modulation
1. base bias modulation
Low frequency modulating signal 은 class c 의 base bias 를
control 하기 위해 사용됨. Base bias voltage 가 conduction
angle 에 영향. 그래서 AM signal 로 output signal 발생.
단점
a. 낮은 efficiency
b. modulation 특성의 비선형성
c. signal level 에 따라 달라지는 base-emitter capacitance 값의 변
화 때문에 amplifier 가 잘못된 동작상태에서 modulation signal
제공.
2. Am signal amplification
SSB transmission 널리 사용.
SSB signal 은 low power level 에서 쉽게 동작하고 바람직한 power
level 에서 선형적 증폭.
Class AB push pull amplifier 로 동작 가능.
3. Collector modulation
Solid state RF amplifier 에서 사용된 amplitude modulation 의 주
요 형태.
AM double sideband (DSB) signal 얻을 수 있다.
In an envelope elimination and restoration (EER) system,
collector modulation can be used to generate any type of AM
signal
1.이 회로의 중요한 이점은 RF amplifier 가 high efficiency 로 동작.
2. 주요 단점은 modulating signal 이 high power level 에서 증폭 되
야 함.
As a result, the efficiency of this amplifier is also important for
the overall efficiency of transmitter.
The modulation transformer must be able to low frequency,
high power signals with low distortion and high efficiency.
Frequency multipliers 는 master oscillator 의 주파수를 multiplier
하거나 modulation index 의 증가시키기 위해 사용된다.
Class C frequency multiplier 는 Class C power amplifier 와 같은
schematic 을 가짐.
The only difference is that the collector resonant circuit is tuned
to the desired harmonics, suppressing all other harmonics
The variation of the maximum collector efficiency max with the
conduction angle c , for a Class C amplifier (n=1), a double
(n=2) , and a tripler (n=3) is shown in Fig 2-102 .
Collector efficiency
decreases as
The multiplying order
N increases
A problem common to any type of frequency multiplier is the
output voltage damping (Fig 2-104)
This effect become stronger as multiplication factor n increase
and output Q decreases.
RF power amplifier instability manifests itself in spurious
oscillations.
These oscillation can occur at frequencies related or unrelated
to the operating frequency (for example, harmonics or
subharmonics ).
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Spurious oscillation can occur under a particular set operating
condition, such as frequency, bias, signal level, load
impedance, and temperature.
Some different oscillation mechanisms may coexist in the
same circuit.
It is very difficult to construct a model of the RF power
amplifier.
Achieving stability may require some sacrifice of gain,
selectivity, or overall efficiency.
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•
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Positive linear feedback can be caused by transistor
interelectrode capacitances and load inductance or by
capacitive or magnetic coupling between the input and output
circuit.
RF power amplifier is always a nonlinear system .Even Class A
amplifier is nonlinear system.
In these case, the quasi-linear approach must used, and the
non linear element of the circuit must be replaced by their
linear equivalent.
The main problem is active device.
The transistor parameters change during the RF cycle.
The conditions required to start or sustain oscillation could
be fulfilled only for certain values of DC-supply voltage and
RF signal level.
In most RF power amplifier it is almost impossible to separate
linear feedback from feedback mechanisms.
Consequently, it is desirable to avoid or to reduce linear
feedback as much as possible.
RF power transistor often dissipate a
significant amount of power that is converted
to heat.
The operating temperature of the junction is
determined by the dissipated power, and the
thermal resistance of the transistor, heatsink,
and ,mounting hardware.
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Experience shows that if the RF chokes and damping effects
are improperly chosen, self-oscillation may appear in RF
power amplifiers.
Am explanation of this behavior is based on nonlinear
oscillation mechanism in the transistor bias network.
A possible positive feedback path may be established in the
circuit. The oscillation appears at a frequency lower than the
intended operating frequency.
To avoid this type of oscillation, it is best to provide resistive
damping in the base bias circuit (Fig 20-106)
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
The theory of circuit with variable parameter show that
oscillations can be generated by periodically varying the
parameter (capacitance or inductance) of one of the energystoring elements of a tuned circuit.
Parametric oscillation usually occurs at a subharmonic of the
circuit operating frequency (f/k, where f is the operating
frequency and k is an integer), although it is no necessary
that the oscillation frequency is an integer submultiple of f.
 Such
oscillation may occur if the base-collector
junction is forced into forward conduction part of
RF cycle.
 The
direct connect between the input and output
tuned circuit may cause oscillation.
Oscillation Caused by the Base Stored Charge may occur in
amplifier in which the transistor saturates during the RF cycle
(for instance, overdiven Class C, mixed-mode, or switchingmode amplifier)
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The transistor remain saturated during the transistor storage
time, which depends on the base and collector current
Q&A
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