What was wrong in designing AM transmitters ? (preliminary)

Fig.1 A simulation result of "Low powered AM modulation" circuit on LTspice (4).

(LTspice(4) is a spice simulator developed by Linear Technology inc.)

Fig1. is an AM/FM modulator component that can generate AM modulated signal voltage or FM modulated signal voltage. It's embedded in LTspice (4) .

In this simulation, I used it as an AM modulator. 

The directive "SINE(40m 40m 1K)" means the amplitude signal voltage as input audio signal is 40mV and DC offset voltage 40mV.  Input signal of sine wave 1KHz is swinged on the DC offset voltage 40mV, and is modulated with 1MHz carrier frequency.

In this case, the AM modulation rate = 100% and quality of the modulated output signal voltage is very good and it is almost perfect.
On the FFT of Fig1, there is almost no distortion in this work and is almost ideal work. 

Fig.2  Block diagram of "Low powered AM modulator"

Fig.2 is a block diagram of "Low powered AM modulator" that explains how it works.

I thought it out by myself from the equation (1) of AM modulation signal voltage.

Vout=(Vdc+x(t))*(Vc*sin(ωc*t)) ... (1)

Here,

x(t): baseband (audio) signal voltage to be fed to the AM modulator .

        On the Fig.1, x(t) = Vin = V3 = V0*cos(2*π*f0*t) ...(2)

Vdc   : DC offset voltage V2. Vdc is often defined as DC 1V in other explanations.  

Adder: Analog signal adder input Vin and V2 and output the added voltage signal as V4.

V1 : Oscillator of sine wave to generate carrier signal for AM signal.

        V1 = Vc*sin(ωc*t), ωc= 2*π*f1*t ...(3)

Mixer (Multiplier) : Analog multiplier. It inputs V4 and V1, then does multiply V4*V1, 

                                  and output V4*V1 to Vout  

Vout : Output signal voltage

As described above, the principle of generating AM signal is very simple.

Once we know the principle beforehand, it makes designing or building AM transmitter/transceiver be quite easier. 

Fig 3.  Collector AM modulation method at the Final transistor used in RJX-601

(Copyright by "Matsushita Denki Corp." in about 197x(?)-198x(?))

RJX-601 is very popular products, many people of Amateur radio licensed love it. 

It can send 1W or 3W of AM or FM E/M wave on the frequency 50MHz to 54MHz.

The specification was the best one on those days.

However it has  some subjects on electronic work in sending AM modulated signal.

When RF power selection is set to 1W, AM modulation is good. 

But it is set to 3W, it generates low modulated AM.

This phenomena was so called "Minus modulation" .

Why "Minus modulation" occurs ?

Following is my analysis of the "collector modulation method at the final transistor".

Fig.4 Abstract circuit of BJT transistor's collector AM modulator

Fig4. is an abstract / equivalent circuit of BJT transistor's collector AM modulator.  

Please watch Fig.4 carefully comparing with Fig.1.

(1) Optimized DC bias voltage of VB is fed to base terminal of the final transistor.

      This bias voltage must be set to class AB or class A to amplify with good linearity. 

      Class C is impossible to use in this application. [2]

(2)RF sine wave voltage source such as 50.6MHz is fed to base terminal of the             

    TR(Transistor). Assume Z of Vrf here = 0 ohm and base terminal has some resistor

    value such as 500 ohm.

(3)Audio Power Amplifier is required to amplify small signal from a microphone to become enough power such as 1W to 5W and drives the 1st side of "Audio power modulation trans".

(4) Vcc = 12V to 13.8V is fed to the 2nd side of "Audio power modulation trans" and amplified audio signal AC voltage rides on the DC Vcc line. This audio modulation signal is connected to "Zc". 

(5) "Zc" is assumed to use ferrite beez such as FB-225. The ferrite beez acts as resistance of hi-Z and inductance value is very low on RF frequency domain. 

It makes the TR to be stable as amplifying device. 

Traditional circuit had used LC tuned tank circuit in the application of vacuum tubes.  But LC tuned tank circuit makes the TR works to be very unstable.  

Because the TR cannot work on such hi-Z stable,  it causes abnormal RF oscillation and TR goes to heaven. It often causes permanent break downs of very expensive TR.

(6) LC Z-matching section must be adjusted to be terminal impedance properly such as 50 ohm.  We can never use LC Hi-Z tank circuit here. 

(Be careful. LC tank circuit is for vacuum tubes but not for TRs.)

(7) Feeding audio amplified signal rides on Vcc=DC 12V to 2 stages of TRs audio amplified is not correct theoretically according to the principle of AM modulation method mentioned above (See the equation(1)).

Fig.5 Visualized work of AM modulation on BJT TR

Fig5. is visualized picture of AM modulation on BJT TR on the final stage of RF power amplifier.

This explanation is based on the traditional design theory of  TR amplifier  with "Load Line method" that was known in 1964.[1]

In this load line design method, TR bias point is set to saturation area of Collector Current "Ic".

Now assume Vcc=12V and there is no audio amplified signal on Vcc on the Load Line.

50.6MHz RF sine voltage signal comes in to TR and amplified along with the Load Line.

There is still no problem.

In this status, input audio signal. Then the Voltage of collector terminal of TR is swinged deeply by the amplified audio signal voltage.

Since Vcc is swinged by the amplified AC voltage, and Load Line is moved by it from left of Vcc and/or to right of Vcc widely.

This means proper bias point of TR moves dynamically and the proper bias to become bad bias point.

As the characteristics of BJT TR, Ic increases with very small amount and it is not linear work with big distortions. The TR can't work as an analog multiplier on this Ic saturated area.

This is the reason why "Minus modulation" occurs.

There is enough reason traditional designed circuit caused "Minus modulation" when 3W output is specified by the power selectable switch. 

There was a reasonable design error.  :-)

How should we correct the traditional design to become well-designed one?

From the equation (1)',  Fig.6 can be introduced as followings. 

Fig. 6  AM modulation by Analog Multiplier

                     Fig. 6A  AM Collector modulation by BJT TR 2N2222 used as an "Analog Multiplier"

(This types of design works with bad quality of AM with distorted AF tone.

The characteristics of BJT TR as an "Analog Multiplier" is not always good.)

Vout=(U0+x(t))*(Vc*sin(ωc*t)) ... (1)'

Here,

x(t): baseband (audio) signal voltage to be fed to the AM modulator .

        On the Fig.6, x(t) = V3 = Va*cos(2*π*f0*t) ...(2)'
V3 is actually audio power amplifier to supply modulation Voltage source with DC offset U0 by the Vcc line (eg. 12V).

U0   : DC offset voltage V2.  (=Vcc=12V)

Adder: Audio power trans here works as an adder.
It inputs V3 and U0, add them and output the voltage signal Vin to Multiplier.

V1 : Oscillator of sine wave to generate carrier signal for AM signal.

        V1 = Vc*sin(ωc*t), ωc= 2*π*f1*t ...(3)'

Mixer (Multiplier) : Analog multiplier. It inputs V1 and Vin, then does multiply V1*Vin, 

                                  and output V1*Vin to Vout  

Vout : Output signal voltage

The equation (1) and (1)' have the same meaning as AM modulators. The deference between them is that they are used in the low power earlier stage of the transmitter or used in the high power last stage.

I've heard that the principle of the AM modulation method by Fig. 6 had been used in the "Plate modulation method" by Final vacuum tube.

I"d like to think, maybe, understandings for multiplier's characteristics of vacuum tube had not always been understood well in those days.

From as my beginners view, TR collector AM modulation method is simply seemed to be exchanged the vacuum tube of plate modulation to a BJT transistor instead.

However, there are big difference of electric characteristics between the vacuum tube and BJT TR.
BJT TR is known as the active device that has the characteristics of CCCS(Current Controlled Current Sources).
Beside, the Vacuum tube is known as the active device that has the characteristics of VCVS(Voltage Controlled Voltage Sources.)

Unfortunately, I've not heard or read of the characteristics as a Multiplier of the old fashioned vacuum tube.
I'm wondering if nobody has been interested in the equation (1) or (1)' in past so long years ?

Once we notice the characteristics of a multiplier is essential for AM modulation from the equation (1) or (1)', we can fix the problem as a subject of Math.


As next step, I thought is about how can I use a BJT transistor as a multiplier.

Generally, BJT transistor's amplifier is designed on the "Load Line" where the collector current is saturated. [1]
In this saturated collector's current working area, BJT TR cannot work as an analog multiplier because the Ic is saturated and increasing VCE cannot increase collector current.

By the way, how does BJT TR work in front of Ic saturated area ?

Fig.7 BJT TR's characteristics before collector current saturated.

Fig.7 shows the BJT TR's characteristics that Ic increases according to VCE increases before Ic is saturated.

Using this Vce area of BJT TR is not recommended by the old fashioned design book.

In the book, Ic was saturated in very low Vce such as 0.3 - 0.5 V.

How it work in the actual BJT TR such as 2SC1815 very popular transistor in Japan ?

  

Fig. 8   Ic vs VCE characteristics of 2SC1815

From the DC sweep of simulation result of Fig.8, BJT TR 2SC1815 has wide range Vce = 0 to 5V with straight linearity of Ic increase.

This implies one (1) 2SC1815 can be used as an analog multiplier.

Fig.9   1 TR 2SC1815 (as an analog multiplier) AM modulation works

Fortunately, it works well. This circuit has benefit that it is not necessary to use a big audio modulation power trans. LM386 can drive the final TR 1815 directly, and AM modulation works well.



Next topics is also serous subject on so called "Base AM modulation method".

Fig.10  Base AM modulation transmitter not work at all

"Base modulated AM method" is very famous even now and the circuit of Fig.10 was found on the internet that seemed to be designed by a professional engineer.
Unfortunately, I could not get any good result on the spice simulation for it.

I had some experiences that the base modulation by a BJT TR didn't work well on the actual circuit. It could never get good result also on it.
I knew that these unwanted situations could be re-confirmed on the LTspice.

Fig.11 After improvement of the circuit of Fig.10

I tried to fix the design errors that I found on the Fig.10 base modulated AM transmitter.
And I managed to work it as Fig.11.
But the quality of modulated RF signal was so dirty.

I know Base AM modulation method has been very famous design but I have no solution to get good quality of AM modulated RF wave even now.
I have lost interest on this method until now.


New design by CQ Pub.inc used Gilbert-cell configured BJT TR AM modulation.

Fig.12 First ever Gilbert-cell type AM modulator
(Copyright by "Transistor Gijyutu" by CQ Pub.inc. 2015)

Analog multiplier configured by Gilbert-cell has invented in US, 1968 as far as I know.
It has very good quality as an analog multiplier and implemented in many DBM (Double Balanced mixer) ICs.
Fig.12 circuit  is the best result of AM modulation method configured by BJT TRs I've ever seen.

Fig.13  Works of C class amplifier

(Copyright by USAF 1963, Mr. Jeff Quitney, Mr. Youtube)

I cannot find application examples of C class amplifier recently.  

I know C class amplifier works with big distortion then it is used to generate harmonic waves as distorted RF output signal such as x3, x4, x5 frequency multiplied. 

I think it is impossible to generate good quality of AM modulation signal from the principle of AM modulation, but very famous Radio magazines for radio fans had been told us that C class amplifier worked very well for AM modulation even until now.

I have no experience that C class amplifier without bios voltage got any good quality of AM. I have no idea to realize to use C class amplifier for AM modulation. 

 From the view of the principle and the characteristics of C class BJT TR amplifier, it's impossible. 

But they say "C class amplifier is very easy to make AM transmitters." 

I cannot find any valid evidence for them.

There are lots of circuit examples of C class ( no bias) amplifiers on the internet even until now but I cannot find any reasonable result from my actual experiments and my calculation by Math. And every simulation by LTspice result tells me that it doesn't work at all. 

Fig.14  Works of AB class amplifier

(Copyright by USAF 1963, Mr. Jeff Quitney, Mr. Youtube)

Class AB is set in RJX-601 on Fig. 2.  Maybe, they knew that Bias voltage was essential for AM modulation by their experiences.

Fig.15  Works of A class amplifier

(Copyright by USAF 1963, Mr. Jeff Quitney, Mr. Youtube)

Class A amplifier requires lots of power consumption even when it is idling. So it is not good for AM transmitter.

This video tells me vaccum tube was used in the linear amplifier, and vacuum tube has a characteristics where there are linear VCVS(Voltage Controlled Voltage Source) working area. 

It also implies vacuum tube has a good characteristics as an analog multiplier.

This characteristics gives reasonable reasons why "plate AM modulation method" works very well.  Beside, BJT TR doesn't have a good characteristics as an analog multiplier. This is big difference between BJT TR and vacuum tube.

Vacuum tubes are often low-estimated as old-fashioned devices but they still have very good linearity and strongness for heavy duty usage for high power RF amplifiers. 

Reliability of vacuum tube can be much better than TR's  in the high power applications.

Fig. 16 is product named "PanaSky 6". I have a few experience to use it when I was a school student. It could send 10W high power AM modulation by vacuum tubes.

An elder student was saying "Don't low-estimate it. It has very good performance." 

Fig. 16 PanaSky 6
(Copyright by Mr. hamlife.jp and  the production vendor of "PanaSky6" )

(Copyright by the production vendor of "PanaSky6" )

I have seen the the product named "FDAM-3" once.  I don't know it well.

(Copyright by ICOM inc. "Inoue Denki-seisakusho-san")

(Copyright by ICOM inc. "Inoue Denki-seisakusho-san")

(Copyright by ICOM inc. "Inoue Denki-seisakusho-san")

Reference:

[1] Amplifiers:

Construction of Load Lines 1971 USAF Electronics Training Film

https://www.youtube.com/watch?v=fc2HihAjq88

[2] Electronics:

"Basic Amplifiers" pt2-2 1963 US Army Training Film

https://www.youtube.com/watch?v=830zDTm55-w

[3] Edwin Howard Armstrong:

The Yonkers Man Who Made Radio and the Alpine Tower

https://www.youtube.com/watch?v=4hZ8BbBJz4w

[4] RCA Radio Model RC Operation

https://www.youtube.com/watch?v=R5tf0G0uB3s

[5] HOW RADIO WORKS - 1943

https://www.youtube.com/watch?v=jqGAneO79lY

( [1] to [5 ]Copyright by USAF 1963, Mr. Jeff Quitney, Mr. Youtube)

[6] MIT 6.003 "Signals and Systems", “Modulation part1, part2” by  Prof. Dennis Freeman

Related documents:

(1) Basic experiments for the principles of AM modulation methods

http://ji1nzl-official.blogspot.jp/2015/07/am.html

(2) Basic experiments for “AM modulation method at Base-terminal of BJT TR”

http://ji1nzl-official.blogspot.jp/2015/09/am_19.html

(3) The principle of “Low powered AM modulation method” (How it works)

http://ji1nzl-official.blogspot.jp/2015/08/amam.html

(4) The principle of “AM modulation method at Collector terminal of Final BJT TR” (How it works)

http://ji1nzl-official.blogspot.jp/2015/08/amam_12.html

(5) New designed AM transmitter by CQ Pub. inc.

http://ji1nzl-official.blogspot.jp/2015/09/cqam.html

(6) Vizualization of AM modulated valtage signal on gpaphs

http://ji1nzl-official.blogspot.jp/2015/12/am.html

(7) Multiplier (Mixer, Frequency converter) related documents

http://ji1nzl-official.blogspot.jp/2015/10/blog-post_14.html

(C) Bakabon Mama and Noboru, Ji1NZL Jul.12, 2016 

Rev 0.1,  Oct.10, 2016
Fig.6 updated: Add an "adder" in Fig.6 to understand easier. 

(Return to index)

IQ直交変調器を用いたウェーバー法によるPSN方式 SSB変調器/送信機の原理

IQ直交変調器を用いたウェーバー法によるPSN方式 SSB変調器/送信機の原理

　概要

従来方式の課題：

PSN方式によるSSB変調方式の課題として次のものがあった。

(1)ベースバンド低周波信号の－90度位相シフト器が、ベースバンド帯域内で利得が一定にならない。

例：

Poly Phase Filterと呼ばれるRC構成による 300Hz - 3KHz 周波数帯域に設計された位相シフト器は、帯域内で利得が変化し、特に低音領域の利得が高く、高い音域で利得が低下するため、太い声で耳障りとなり、高い音が弱くなり、聞き取りにくい音声になる。

(2)同Poly Phase Filterは、設計帯域を外れた周波数帯域 20Hz - 300Hz の低い音の位相ずれが-90度を維持できず、低音域がおかしな音になる。

こうした課題を解決する方式として、Poly Phase Filterを使用しないウェーバー法(Weaver Method)が知られていたが、その動作原理説明は、実回路開示や、難解なタイミング図と難しい長い文章による解説で、方式を正確に理解することが著しく困難だった。

(3)ウェーバ法による方式上の課題（問題点）が開示されていなかった。

(4)方式が不明または曖昧な理解であるため、SDRの設計ができない。

ここでは、以上の課題を反省し、これまでの課題を克服するため、計算式によりウェーバー法を導出して求め、やさしく、かつ正確に同方式を定義し、SDR設計に直接使用できる設計内容を明らかにする。

2. 構成

図1. による。

図1

3. 方式の計算式導出と説明

説明は次の文書による。

”The principle of SSB modulator / transmitter of “Weaver PSN method 
by using “IQ feeder” and “IQ modulator”  (Weaver’s PSN method)
http://ji1nzl-official.blogspot.jp/2016/07/the-principle-of-ssb-modulator.html


4. 課題

項番号 3.により、ウェーバー方式には設計上、次の課題の存在が明らかになった。

(1) 現在SDRに多用されているIQ直交変調器が、ウェーバー方式にもそのまま使用できる。
ウェーバー方式では、IQ変調器に、90度位相差があるSSBの2信号I,Q信号を与えるだけで、SSB(USB/LSB)の変調・復調器が実現できる。

(2) ウェーバ方式で利用されるLPF(Low Pass Filter)は、LSB,USBの不要成分を除去するため、良好なフィルタのキレ具合と、帯域内一定の群遅延特性を持つ必要がある。

これは、FIR,IIRフィルタの信号処理で実現できる。

(3) 上記LPFは、アナログ回路では、良好な特性を得る回路実現に難易度が伴う可能性がある。

(4) ウェーバー方式は、音声などのベースバンド信号を一旦、40KHz程度の中間周波数帯に引き上げるため、この局部は発振器周波数だけ、第二局発の発振周波数に対し、キャリア周波数がIF周波数分だけシフトする。

受信機側では、SSB復調時に、キャリアが無いため、そのシフト分は気づくことは無いが、送信機の周波数表示処理は、このシフト周波数をずらして表示する加算または減算処理が必要となる。

(5)上記LPFは、HPFで交代するように方式変更も可能である。ただし、キャリアシフト量は変化する。

付録:

A. SSB/CW SDRトランシーバの実現例

　　　　　　　G11 Gunu Radio based SDR Transceiver

                               Designed by Goran in Eu. (Respective copyright reserved) 
               

(C) Noboru, Ji1NZL, Jun.29, 2016

Rev.0.0 July 2, 2016 初版文書作成　Noboru Noboru .AE35.macbook

The principle of SSB modulator / transmitter of “Weaver PSN method by using “IQ feeder” and “IQ modulator” (Weaver’s PSN method) (preliminary)

The principle of SSB modulator / transmitter of “Weaver PSN method 
by using “IQ feeder” and “IQ modulator”  (Weaver’s PSN method) (preliminary)

1. Architecture

“Weaver PSN method modulator / transmitter” has 3 functional blocks.

(A) “Baseband signal generator” … Eg. Microphone and/or with small signal amplifier(s)

(B) “IQ feeder for baseband signal” inputs baseband signal from “Baseband signal generator” , converts it IF frequency stage such as 10KHz to 40KHz and outputs two orthogonal voltage signals “I” and “Q”.

(C)“IQ modulator” inputs two port of orthogonal signals “I” and “Q” and outputs to 1 port of SSB modulated signal.

2. How it works

(A) Baseband signal generator

    Assume V1 is “baseband signal” to be input as audio signal. 
    (eg. We can use microphone to input V1.)

    V1 = Vs*sin(ωs*t) …(1)
    here ωs = 2πfs  …(2) 
          fs [Hz] is 0 to 20KHz Frequency of baseband signal on Audio frequency        ( 2.6KHz to 3.0KHz is preferred in the actual application as the maximum  
          frequency of baseband AF signal. )

(B) IQ feeder for baseband signal

OSC1 generates ωc1[rad*Hz] sin wave voltage. 
ωc1 is fixed frequency and OSC1 is used for first frequency conversion. 

Vosc1 = Vc1*sin(ωc1*t) …(3)
here ωc1 = 2πfc1 …(4) 
 fc [Hz] is set to IF frequency such as 40KHz to covert baseband frequency ω1  
          to ωc-ωs or ωc+ωs.

Shift Vosc1 signal to be -90 deg. by “-90 deg. Shifter” to get V2.

V2 = Vc1*sin(ωc1*t-π/2) = -Vc1*cos(ωc1*t) …(5)

Get V3 by multiplying V1 and Vosc1.

V3= V1*Vosc1 = (Vs*sin(ωs*t)) * (Vc1*sin(ωc1*t)) 
  = Vs*Vc1*sin(ωs*t) * sin(ωc1*t) 
    =Vs*Vc1*(1/2){ cos(ωc1*t+ωs*t) - cos(ωc1*t-ωs*t) }
    =(1/2)*(Vs*Vc1)*{ cos((ωc1+ωs)*t)) - cos((ωc1-ωs)*t)) } …(6)

Set cut frequency ωcut of LPF to be ωcut < ωc1, 
then cos((ωc1+ωs)*t) can be removed. (->*Note1)

Then get V4,
V4 = -(1/2)*(Vs*Vc1)*cos((ωc1-ωs)*t)) …(7)

...Output of “I” came out here.

Get V5 by multiplying V1 and V2.
V5= V1*V2 
= (Vs*sin(ωs*t)) * (-Vc1*cos(ωc1*t)) = -Vs*Vc1*sin(ωs*t) * cos(ωc1*t) 
    = -Vs*Vc1*(1/2){sin((ωc1*t+ωs*t) + sin((ωc1*t-ωs*t))}
    = -Vs*Vc1*(1/2){sin((ωc1+ωs)*t)  + sin((ωc1-ωs)*t))} …(8)

Set cut frequency ωcut of LPF to be ωcut < ωc1, 
then sin((ωc1+ωs)*t)  can be removed. (->*Note1’)

Then get V6
V6 = -(1/2)*Vs*Vc1*sin((ωc1-ωs)*t)) …(9)

... Output of “Q” came out here.

(C) IQ modulator

Input voltage of “I” and “Q” for “IQ modulator (C)” here are given 
as output of “IQ baseband feeder (B)”. 

OSC generates ωc2[rad*Hz] sin wave voltage.
Vosc2 = Vc2*sin(ωc2*t) …(10)
here ωc2 = 2πfc2 …(11) 
          fc2 [Hz] can be set to RF frequency of VFO such as 14MHz.

Shift Vosc2 signal (10) to be -90 deg. by “-90 deg. Shifter” and get V7. 

V7 = Vc2*sin(ωc2*t-π/2) = -Vc2*cos(ωc2*t) …(12)

Get V8 by multiplying V4 and V7.

V8= V4*V7 = (-(1/2)*(Vs*Vc1)*cos( (ωc1-ωs)*t)) ) * (-Vc2*cos(ωc2*t)) 
                  = (1/2)*Vs*Vc1*Vc2*cos( (ωc1-ωs)*t)) ) * cos(ωc2*t) …(13)


Get V9 by multiplying V6 and Vosc2.
V9 = V6*Vosc2 = (1/2)*Vs*Vc1*cos((ωc1-ωs)*t)) * Vc2*sin(ωc2*t)
    =  (1/2)*Vs*Vc1*Vc2*sin((ωc1-ωs)*t)) * sin(ωc2*t) …(14)

When “Adder” used before Vout,
Vout = V8+V9 =  (1/2)*Vs*Vc1*Vc2*cos((ωc1-ωs)*t)))*cos(ωc2*t)      
                        + (1/2)*Vs*Vc1*Vc2*sin((ωc1-ωs)*t)) * sin(ωc2*t)
= (1/2)*Vs*Vc1*Vc2*(cos((ωc1-ωs)*t)))*cos(ωc2*t) 
  + sin((ωc1-ωs)*t))*sin(ωc2*t)
= (1/2)*Vs*Vc1*Vc2*cos( (ωc1-ωs)*t - ωc2)*t) )
= (1/2)*Vs*Vc1*Vc2*cos( (ωc1-ωc2)-ωs)*t )  … here cos() is even function then 
= (1/2)*Vs*Vc1*Vc2*cos( (ωc2-ωc1)+ωs)*t ) …(15)

  … This (15) means USB generated as output signal Vout. 
     (15) is USB signal and Carrier ωc2-ωc1 signal voltage is removed here
      and receivers have to set tuning Carrier frequency to be ωc2-ωc1.
            -> (*Note 2)

When “Subtracter” used before Vout,

Vout = V9-V8 = (1/2)*Vs*Vc1*Vc2*sin((ωc1-ωs)*t)) *sin(ωc2*t)    
             - (1/2)*Vs*Vc1*Vc2*cos((ωc1-ωs)*t)) *cos(ωc2*t)
 = -(1/2)*Vs*Vc1*Vc2*{cos((ωc1-ωs)*t-ωc2)*t)-sin((ωc1-ωs)*t))*sin(ωc2*t) }  
 = -(1/2)*Vs*Vc1*Vc2*({cos( ((ωc1-ωs)+ωc2))*t )  
 = -(1/2)*Vs*Vc1*Vc2*({cos( ((ωc2+ωc1) -ωs))*t ) …(16)

 … This (16) means LSB generated as output signal Vout. 
    (16) is LSB signal and Carrier ωc2+ωc1 signal voltage is removed here
    and the receiver has to set running Carrier frequency to be ωc2+ωc1.
          -> (*Note 3)

“Weaver’s PSN method” by using “IQ baseband feeder” and “IQ modulator” 
is proved to generate SSB modulated signal ( USB or LSB).

-> (*Note1, Note1’) : 
DSB(Double sided band) is generated by the Multiplier 
on the “IQ feeder” and  LPF can remove USB band theoretically. 

However Characteristics of “Shape factor” and “signal group phase delay” 
on the IF signal band is very important to design the LPF.

Otherwise, unwanted signal may remain on the IF signal line V4 or V6. 
This subject is derived from the principle of the “Weaver’s PSN method” 
but DSP filter’s characteristics can solve this subject.
(Analog type of LPF or HPF may be difficult to solve it.)

HPF can be used instead of LPF on this method as the same principle.

-> (*Note 2)(*Note3) ; 
    SSB receivers have to their tuning frequency to become shifted  
    carrier by Vosc1. 
    This subject can solve easily by the tuning frequency adjustment  
    at SSB receivers side.

(C) Noboru, Ji1NZL, Jun.29, 2016

Rev.0.1 : 
Add missing variable "Vc1" in the equation (16) (mistypes) Jul.5, 2016
(No change of the theory itself. I'm sorry for it.)

Rev.0.1A: 
Changed variable ωc2 to ωc1 in the equation (16) (mistypes) Jul.6,2016
(No change of the theory itself. I'm sorry for it.)

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IQ変調器（直交変調器）を使ったPSN法によるSSB信号の生成方式 (日本語版)

IQ変調器（直交変調器）を使ったPSN法によるSSB信号の生成方式　(日本語版)

概要

現在は、PSN方式がDSP信号処理で実現されている。

PSN方式の動作説明は、これまで長い間、回路信号の図と難解な長い文章で表現されてきた。

このため、その動作原理の理解が難しく、曖昧であった。

ここでは、PSN方式が、IQ変調器を使って構成できることを図解し、SSB(USB/LSB)が生成される動作原理を、数式で表現する方法を用いる。

そうすることで、原理説明の曖昧さを無くし、シンプルでやさしく理解できるようにした。

また数式で変調方式を表現することで、SDR（ソフトウェアラジオ・無線）のソフトウェア実現方式(数値演算変調方式)を明確にした。

1.　構成

IQ直交変調器を使用したPSN変調器を図1に示す。

図1 IQ直交変調器を使用したPSN変調器

以下、図1中の構成要素について説明する。

ベースバンド信号電圧入力源 V1（例：マイクロフォンをアンプで電圧増幅した電圧信号源）

(2) -90度位相シフト回路1:　信号V1の位相を-90度シフトする回路

(3) 局部発振器 Vosc : キャリア周波数 fc[Hz]の発振電圧を発生する回路

(4) -90度位相シフト回路2:　局部発振器電圧 Voscの位相を-90度シフトする回路

(5) 乗算器1: (1)の電圧V1と、(4)の-90度位相シフト電圧信号を入力し、乗算し、V4へ出力

　ie. V4 := V1*V3

(6) 乗算器2: (2)の-90度位相シフトした電圧V2と、(3)の局部発振器Voscを乗算し、V5へ出力

(7) 加算器または減算器：乗算器1の出力電圧V4と、乗算器2の出力電圧を加算または減算し、Voutへ出力

　ie. Vout := V5 + V4  (USB生成時）

　　　または

     Vout := V5 - V4　(LSB生成時)

以上の要素で構成する。

このうち、IQ直交変調器は、(3)(4)(5)(6)(7)の各要素を接続して構成する。

PSN方式SSB変調器は、この直交変調器(3)(4)(5)(6)に、(1)(2)の構成で生成するI信号、Q信号生成器を接続したものとなる。

2. 処理方式

2.1 要素別の処理説明

(a)局部発振器Voscを発振させ、出力電圧を乗算器2と、-90度位相シフト回路2の入力とする。

(b)-90度位相シフト回路2により、Vosc信号の位相を-90度シフトし、乗算器1の入力とする。

(c)ベースバンド信号電圧入力源 V1を入力し、乗算器1の入力とし、かつ、-90度位相シフト回路1の入力とする。

(d)乗算器1は、 V4 := V1*V3    を実行する。

(e)乗算器2は、 V5 := V2*Vosc を実行する。

(f)加算器は、 Vout := V5 +V4 を実行する。または、減算器は、 Vout := V5-V4 を実行する。

(a)～(f)を並列処理すれば、SSB信号(USBまたはLSB)が、Voutに生成される。

2.2 計算式による説明

The principle to generate SSB modulated signal by using IQ modulator (PSN method)

Assume V1 is “baseband signal” to be input as audio signal.

(eg. we can use microphone to input V1.)

V1 = Vs*sin(ωs*t) …(1)

 here ωs = 2πfs  …(2)

         fs [Hz] is 0 to 20KHz Frequency of baseband signal on Audio frequency

Shift V1 signal to be -90 deg. by “-90 deg. Shifter”.

V2 = Vs*sin(ωs*t-π/2) = -Vs*cos(ωs*t) …(3)

OSC generates ωc[rad*Hz] sin wave voltage.

Vosc = Vr*sin(ωc*t) …(4)

here ωc = 2πfc …(5)

         fc [Hz] is set to RF frequency such as 9MHz so called “Carrier frequency”.

Shift Vosc signal (4) to be -90 deg. by “-90 deg. Shifter” and get V3.

V3 = Vr*sin(ωc*t-π/2) = -Vr*cos(ωc*t) …(6)

Get V4 by multiplying V1 and V3.

V4= V1*V3 = Vs*sin(ωs*t) * (-Vr*cos(ωc*t)) = -Vs*Vr*sin(ωs*t) * cos(ωc*t) …(7)

Get V5 by multiplying V2 and Vosc.

V5 = V2*Vosc = -Vs*cos(ωs*t) * Vr*sin(ωc*t) = -Vs*Vr*cos(ωs*t) *sin(ωc*t) …(8)

When “Adder” used before Vout,

Vout = V4+V5 = -Vs*Vr*sin(ωs*t) * cos(ωc*t) -Vs*Vr*cos(ωs*t) *sin(ωc*t)

       = -Vs*Vr* (sin(ωs*t) * cos(ωc*t)+cos(ωs*t) *sin(ωc*t))

       = -Vs*Vr* (sin(ωs*t+ωc*t) ) = -Vs*Vr*sin((ωs+ωc)*t)  …(9)

       … This (9) means USB generated as output signal Vout.

           (9) is USB signal and Carrier ωc signal voltage is removed here.

When “Subtracter” used before Vout,

Vout = V5-V4 = -Vs*Vr*sin(ωs*t) * cos(ωc*t) + Vs*Vr*cos(ωs*t) *sin(ωc*t)

       = -Vs*Vr* (sin(ωs*t) * cos(ωc*t) - cos(ωs*t) *sin(ωc*t))

       = -Vs*Vr* (sin(ωc*t-ωs*t ) = -Vs*Vr* sin((ωc-ωs)*t)  …(10)

       … This (10) means LSB generated as output signal Vout.

         (10) is LSB signal and Carrier ωc signal voltage is removed here.

“PSN method” by using “IQ modulator” is proved to generate SSB modulated signal

( USB or LSB).

(C) Noboru, Ji1NZL, Jun.21, 2016

付録

A. SSB変調信号とは

中波ラジオ、短波ラジオ、航空無線では、AM変調(振幅変調)による電波が、音声通信・ラジオ放送に使用されている。

AM信号は、キャリア周波数を中心にして、LSB帯域の変調信号、USB帯域の変調信号で構成されている。

SSB信号は、AM信号から、キャリア信号と、USB帯域またはLSB帯域のどちらかの変調信号のみを利用する。

SSB信号は、送信機ではAM信号中の、キャリア信号と片側のUSBまたはLSB帯域信号を増幅すれば良いので、変調波信号の送信回路で消費される送信機の消費電流を大幅に省電力化できる。

また、受信時は、SSB信号は、受信信号が微弱でも、非常に良好な了解度が得られるメリットもある。

こうしたSSB変調信号は、省電力で遠距離通信に向いているので広く普及している。

B.　SSB変調回路開発の歴史

従来技術として次のものがある。

(1)リング変調回路＋水晶フィルタによるSSB変調方式　:　

送受信機回路は、リング変調回路のDSB信号出力を、3KHz帯域ほどの水晶フィルタでDSB信号の必要なUSB帯域成分または、LSB帯域成分を通過させ、余分なUSB帯域、LSB帯域を除去し、そのSSB信号をリニア増幅して送信する方式。

1970年～1990年に普及。

製品例： TS-520X/D, TS-820X/D, TS-830X/D

(2) アナログPSN方式：

アナログ回路構成によるPSN(Phase Shift Network)方式が知られていたが、90度位相シフト回路の電気的特性で、利用周波数帯域内で利得が変化してしまう等の課題があり、あまり普及しなかった。

(3) デジタル数値演算変調方式:

現在主流の方式。無線機に実装されているSSB変調は、数値演算変調方式という言葉で表現されたDSP信号プログラム処理により、変調・復調ができる。

(4)携帯電話のノキア社が、1997年にIQ変調器・復調器の特許を出願していることが分かった。

I/Q modulator and demodulator EP 0546719 B1

実施例では、乗算器にダイオード・リング変調器/復調器を使用しており、最新型ではないが、複素数信号処理の概念が明らかになった世界初または初期の発明かもしれない。

C. LTspice によるSSB変調信号生成の計算実験

LTspice によるSSB変調信号生成の計算実験

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